Coordinate Geometry Class 9 MCQ Maths Chapter 3

Coordinate Geometry MCQ for Class 9 (Multiple Choice Questions with Solutions)

1.   The point (2, 3) is at a distance of _______ units from x-axis :

(A) 2

(B) 5

(C) 3

(D) None of these

Ans.       (C)

Sol.         

                The distance of point (2, 3) from x-axis is 3 units. 

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2.   The point (– 3, 2) belongs to :

(A) Ist quadrant

(B) IInd quadrant

(C) IIIrd quadrant

(D) IVth quadrant

Ans.     (B)

Sol.       

                The point (–3, 2) belongs to ‘Second quadrant’.

(as  x < 0  &  y > 0)

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3.    The area of a square whose vertices are (– 3, 4), (–3, 1) (0, 1) and (0, 4) is :

(A) \sqrt {18} sq. units

(B) 18 sq. units

(C) 15 sq. units

(D) None of these

Ans.      (D)

Sol.       

                Length of side of square = BC = AB = AD = CD = \sqrt 9  = 3

⇒              Area of square = 3² = 9 sq. units

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4.    The points (a, a) (– a, – a) and ( - \sqrt 3 a, \sqrt 3 a) form the vertices of an :

(A) Scalene triangle

(B) Right angled triangle

(C) Isosceles right angled triangle

(D) Equilateral triangle

Ans.         (D)

Sol.    The points A(a, a), B(–a, –a), C ( - \sqrt 3 a,\,\,\sqrt 3 a)

⇒       AB = \sqrt {4{a^2} + 4{a^2}}  = 2a\sqrt 2 , BC = 2a\sqrt 2   ,  CA = 2a\sqrt 2

⇒        ΔABC is an equilateral triangle.

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5.    If (2, 1), (4, 5), (–1, –3) are the mid points of the sides of a triangle, then the coordinates of its vertices are :

(A) (–3, –7) (17, 9) (1, 1)

(B) (–3, 7) (7, 9) (–1, –1)

(C) (–3, –7) (7, 9) (1, 1)

(D) None of these

Ans.         (C)

Sol.         Let    A ≡ (x₁, y₁) & B ≡ (x₂, y₂)

‡       D(2, 1) divides AB in ratio 1 : 1.

⇒      2 = \frac{{{x_2} + {x_1}}}{2} \Rightarrow {x_1} + {x_2} = 4    . . .(1)

&       1 = \frac{{{y_2} + {y_1}}}{2} \Rightarrow {y_1} + {y_2} = 2    . . .(2)

Similarly  x₂ + x₃ = 8       . . .(3)

y₂ + y₃ = 10                     . . .(4)

x₁ + x₃ = –2                     . . .(5)

y₁ + y₃ = –6                     . . .(6)

Now solving (1), (3) & (5) we get : x₁ = –3, x₂ = 7; x₃ = 1 & solving (2), (4) & (6)

we get :  y₁ = –7; y₂ = 9;  y₃ = 1

⇒     Vertices are :  (–3, –7), (7, 9) & (1, 1)

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6.   The coordinates of A and B are (–3, 9) and (1, a+4) respectively. The mid point of AB is (–1, 1), then the value of a is :

(A) –2

(B) 2

(C) 11

(D) –11

Ans.      (D)

Sol.               

‡       P(–1, 1) is mid point of AB

⇒      1 = \frac{{9 + a + 4}}{2}  ⇒ 13 + a = 2  ⇒ a = –11

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7.    The centroid of the triangle whose vertices are (4, –8), (–9, 7) and (8, 13) is :

(A) (1, 4)

(B) (1, 3)

(C) (1, 5)

(D) (1, 9)

Ans.       (A)

Sol.        Vertices of triangle are (4, –8), (–9, 7) & (8, 13)

⇒     Centroid = \left( {\frac{{4 - 9 + 8}}{3},\,\,\frac{{ - 8 + 7 + 13}}{3}} \right)

= (1, 4)

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8.    The mid point of the line segment AB  shown in the figure is (4, – 3). Then the coordinates of A and B are :

(A) (8, 0) and (0, – 6)

(B) (0, 8) and (0, – 6)

(C) (8, 0) and (– 6, 0)

(D) None of these

Ans.      (A)

Sol.        Let    A ≡ (x, 0) & B = (0, y)

⇒     4 = x/2  ⇒  x = 8

&     y/2 = –3  ⇒ y = –6

⇒     A ≡ (8, 0) & B ≡(0, –6)

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9.    The ratio in which (4, 5) divides the line joining (2, 3) and (7, 8) is :

(A) 2 : 3

(B) –2 : 3

(C) 3 : 1

(D) 2 : –3

Ans.       (A)

Sol.       Let    P(2, 3) & Q(7, 8) is divided by R(4, 5) in ratio m : n

⇒     \frac{{2n + 7m}}{{m + n}} = 4

⇒     2n + 7m = 4m + 4n

                ⇒      2n – 3m = 0

&       \frac{{3n + 8m}}{{m + n}} = 5  ⇒ 3n + 8m = 5m + 5n   ⇒  2n – 3m = 0

⇒     Required ratio is 2 : 3

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10.    The area of triangle formed by (a, b+c), (b, c+a) and (c, a+b) is :

(A) (a + b + c)

(B) abc

(C) (a + b + c)²

(D) 0

Ans.     (D)

Sol.        Area of triangle formed by (a, b + c), (b, c + a) & (c, a + b) is

\frac{1}{2}[a(c + a - a - b) - (b + c)\,(b - c) + (b)\,(a + b) - (c + a)\,c] = \frac{1}{2}[a(c - b) - ({b^2} - {c^2}) + ab + {b^2} - ac - {c^2}] = \frac{1}{2}[ac - ab - {b^2} + {c^2} + ab + {b^2} - ac - {c^2}] = \frac{1}{2}[0] = 0 sq. units

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11.   If  x = – 3, y = – 2 is a solution of 4x – ky = 5 then find 2k + 3 :

(A) 15                                            

(B) \frac{{17}}{2}

(C) 17                                            

(D) 20

Ans.     (D)

Sol.      4(–3) – k(–2)  = 5.

    ⇒ – 12 + 2k = 5 ⇒ 2 k = 17,  k = \frac{{17}}{2}

            i.e.,   2k + 3 = 2\left( {\frac{{17}}{2}} \right) + 3 = 20 .

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12.   Find the value of  x  if  y = 7 in given equation 4x + 5y = 7 :                                        

(A) –3                                            

(B) –7

(C) –8                                            

(D) +7

Ans.     (B)

Sol.      4x + 5 (7)  = 7.

            4x  = 7 – 35 = – 28.

             x = – 7.

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13.   Find the value of x in terms of y in given equation 3x\, - \,y\, + \,7\, = \,0 :                

(A) \frac{{y\, - \,7}}{3}                        

(B) \frac{{y\, + \,7}}{3}

(C) \frac{{ - y\, + \,7}}{3}                            

(D) \frac{{ - y\, - \,7}}{3}

Ans.     (A)

Sol.      3x – y + 7 = 0

            3x = y – 7

            x  =\frac{{y\, - \,7}}{3}.

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14.    Find the value of y in terms of x in given equation 8x – 7y = 12 :                                  

(A) \frac{{8x\, + \,12}}{7}                          

(B)  \frac{{8x\, - \,12}}{7}

(C) \frac{{ - 8x\, + \,12}}{7}                               

(D) \frac{{ - 8x\, - \,12}}{7}

Ans.     (B)

Sol.      8x – 7y  = 12

            7y  = 8x – 12

            y  =\frac{{8x\, - \,12}}{7} .

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15.   Linear equation 2x + 3 = 7 is :         

(A) Parallel to x – axis

(B) Parallel to y – axis

(C) Passes through origin making an angle of 45°  with corrdinate axes :

(D) None of these 

Ans.     (B)

Sol.      2x + 3  = 7

        ⇒ 2x = 4 ⇒ x = 2, which is parallel to y-axis.

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16.   The linear equation  y = 2x + 3 cuts the y axis at:                                                           

(A) (0,3)                                                          

(B) (0, 2)

(C)  \left( {\frac{3}{2}\,,\,\,0} \right)                                                          

(D)  \left( {\frac{2}{3}\,,\,\,0} \right)

Ans.     (A)

Sol.      at y-axis  x = 0

            i.e., y = 2 × 0 + 3 = 3. i.e., (0, 3).

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17.   (2, 1) is  a point which belongs to the line :       

(A) x = y                                                         

(B) y = x +1

(C) 2y = x                                                       

(D) xy = 1

Ans.     (C)

Sol.      In given option (C)  2 × 1 = 2.

                                           L.H.S. = R.H.S.

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18.   If (5, k) is solution of 2x + y – 6 = 0, then the value of k is equal to :

(A) 6                                              

(B) 4

(C) – 3                                           

(D) – 4

Ans.     (D)

Sol.      2 × 5 + k – 6 = 0

        ⇒ k = 6 – 10 = – 4.

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19.  If a + b = 5 and 3a + 2b = 20, then 3a + b will be :

(A) 25                                            

(B) 20

(C) 15                                            

(D) 10

Ans.     (A)

Sol.      Let  a + b = 5                      …… (1)

            3a + 2b = 20                       …… (2)

            In equation (2)   a + 2 (a + b) = 20

             a + 2 × 5 = 20 ⇒ a = 10.

            Now     3a + b = 2a + a + b = 20 + 5 = 25.

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20.   Which of the following respective values of x and y satisfy the following equations I and II?

1. 3x + y = 19
2. x – y = 9

(A) 7, 2                                          

(B) 7, – 2

(C) – 7, 2                                                        

(D) – 7, – 2

Ans.     (B)

Sol.      3x + y = 19                         …… (1)

            x – y = 9                             …… (2)

            adding (1) and (2)

            4x = 28 ⇒ x = 7

            then  7 – y = 9 ⇒ y = – 2

            i.e., x = 7 and y = – 2.

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21.    Find out which of the following equaiton have x = 2, y = 1 as a solution :                     

(A) 2x – 5y = 9                                                

(B) 5x + 3y = 14

(C) 2x + 3y = 7                                                

(D) None of these

Ans.     (C)

Sol.      2x + 3y = 7

            L.H.S. = 2 × 2 + 3 × 1 = 4 + 3 = 7 = R.H.S.

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22.   Which one of the following is the solution of  linear equation 4x - \,3y\, = \,8 : 

(A) x = 3, y = 2                                                

(B) x = 5,  y = 4

(C) x = 16, y = –8                                            

(D) None of these                                           

Ans.     (B)

Sol.      x = 5,  y = 4

            L.H.S. = 4 × 5 – 3 × 4 = 20 – 12 = 8 = R.H.S.

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23.    The straight line 2x + 3y = 0 :                                                                                      

(A) Is parallel to the x-axis                                                                                          

(B) Is parallel to the y-axis                               

(C) Cuts intercepts of  2 units from x-axis and 3 from y-axis                                        

(D) Passes through the origin (0, 0)

Ans.     (D)

Sol.      Passes through the origin (0, 0), cause 2 × 0 + 3 × 0 = 0 = R.H.S.

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24.   The graph of the equation 3x + 4y = 8 intersect the x axis at :                                      

(A) (2, 0)

(B) \left( {\frac{8}{3},\,0} \right)

(C) (0, 2)                                                         

(D) \left( {0,\,\,\frac{8}{3}} \right)

Ans.     (B)

Sol.      at x-axis y = 0

            i.e.,  3x + 4 × 0= 8  ⇒ x = \frac{8}{3}

            i.e., \left( {\frac{8}{3},\,0} \right).

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25.   If (3,4) is one of the solutions of 3x – 5y = a then a is :                                                  

(A) 11  

(B) –11

(C) 21  

(D) 7

Ans.     (B)

Sol.      3(3) – 5(4) = a

    ⇒      a =  9 – 20 = – 11.

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26.    Which of the following is graph of  x + y = 0:   

(A)   

(B)       

(C)       

(D) 

Ans.     (C)

Sol.    

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27.   The graph of equation 3x + 5y = 15 will intersect the y-axis at the point :

(A) (3, 5)                                             

(B) (5, 3)

(C) (0, 3)                                             

(D) (5, 0)

Ans.     (C)

Sol.      at y-axis x = 0.

            i.e., 3 × 0 + 5y = 15 ⇒y = 3, i.e., (0, 3).

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28.   If x = 1, y = –1 is a solution of  5x + 2ay = 3a then find a :

(A) 0    

(B) –1

(C) 1    

(D) Can’t be determined

Ans.     (C)

Sol.      5 × 1 + 2a (–1) = 3a.

            5 – 2a = 3a ⇒ 5a = 5 ⇒ a = 1.

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29.   If ax + by + c = 0, passes through origin, then :

(A) a = 0                                                         

(B) c = 0

(C) b = 0                                                         

(D) Can’t say

Ans.     (B)

Sol.      a × 0 + b × 0 + c = 0  ⇒ c = 0.

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30.   If 2a + 5b + c = 0, then a point on the line ax + by + c = 0 is :                                      

(A) (5, 2)                                                         

(B) (2, 5)

(C) (0, 0)                                                         

(D) None of these

Ans.     (B)

Sol.      From given option (B)                          

            x = 2 and y = 5

            2x + 5y + c = 0. (It is already given).

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31.   The equation  of the  line parallel to y-axis is:  

(A) y = –2                                                      

(B) y = 0  

(C) y = 5                                                        

(D) x = –4                                      

Ans.     (D)

Sol.      x = –4

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32.    The equation of the  line passing through the origin is :                                                

(A) y = 2                                                        

(B) x = 4 

(C) y = 5x                                                      

(D) None of these

Ans.     (C)

Sol.      y = 5x

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33.   The line x = 2 passes through the points (s):                                                                

(A) (2, 0)                                                        

(B) (2,–1)  

(C) (2, 1000)                                                   

(D) All of these

Ans.     (D)

Sol.      All of these

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34.   Find the perpendicular distance of x-axis from  the point P(–3, –4) :                             

(A) –4                                                

(B) –3

(C) 3                                                  

(D) 4

Ans.     (D)

Sol.      4     

       

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35.   The distance of the point P(6,4) from y-axis is :                                                             

(A) 6 units                                                      

(B) 8 units

(C) 10 units                                                    

(D) 14 units

Ans.     (A)

Sol.      6 units

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36.   The distance of the point A (4, 3) from the x-axis :                                                         

(A) 3 units                                                      

(B) 4 units

(C) 5 units                                                      

(D) 6 units

Ans.     (A)

Sol.      3 units    

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37.   If three points (1,1),(4,4) and (7,7) are ploted on a graph paper, then on joining them we get a :                

(A) Triangle                                                    

(B) Straight line

(C) Equilateral triangle                                    

(D) Can’t be determined

Ans.     (B)

Sol.      Straight line

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38.   The graph of  x = 6 is a straight line :              

(A) Intersects both the axes                            

(B) Parallel to y-axis                       

(C) Parallel to x-axis                                       

(D) Passing through the origin

Ans.     (B)

Sol.      Parallel to y-axis

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39.   Find which of the following equation have x = 2, y = 1 as a solution :                             

(A) 2x + y = 5                                                 

(B) 2x + 4y = – 1

(C) 2x – 3y = 15                                             

(D) None of these

Ans.     (A)

Sol.      2x + y = 5

            L.H.S.  2(2) + 1 = 5 = R.H.S.

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40.   In which quadrant do the point Q(3, 2) lie?

(A) I                                                 

(B) II

(C) III                                               

(D) IV

Ans.     (A)

Sol.    

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41.   If 3x – 5 y = 5 and \frac{x}{{x + y}}=\frac{5}{7}, then what is the value of x – y?                             

(A) 9                                              

(B) 6

(C) 4                                              

(D) 3

Ans.     (D)

Sol.      Let  3x – 5y = 5                   …… (1)

            and \frac{x}{{x + y}} = \frac{5}{7}                                     …… (2)

            from equation (2)     7x  = 5x + 5y

                                           2x  = 5y

            Now in equation (1)

                            3x – 2x  = 5

                           x = 5 then y = 2

            i.e.,         x – y = 5 – 2 = 3.

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42.   If  2x + 3y = 47 and 11x = 7y,  then what is the value of  y – x ?                                     

(A) 4                                              

(B) 5

(C) 6                                              

(D) 7

Ans.     (A)

Sol.      2x + 3 y = 47                       …… (1)

            11x – 7y = 0                        …… (2)

            from equation (2)   y =\frac{{11x}}{7}.

            Now in equation (1)

                       2x +\frac{{33x}}{7} = 47

            ⇒       \frac{{14x + 33x}}{7} = 47

            ⇒      \frac{{47x}}{7} = 47

            ⇒     x = 7 then, y = \frac{{11 \times 7}}{7} = 11

            i.e.,    y – x   = 11 – 7 = 4.

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43.    The solution of the simultaneous equations\frac{1}{2}x + \frac{1}{3}y  = 2 and x + y = 1 is :        

(A) x = 1, y = 0                                                

(B) x = 0, y = 1                             

(C) x = 10, y = – 9                                           

(D) x = \frac{2}{3} , y = \frac{3}{2}

Ans.     (C)

Sol.      Let      3x + 2y = 12             …… (1)

            and     x + y = 1                  …… (2)

            In eqaution (1)  x + 2 (x + y)  = 12 ⇒ x + 2 (1) = 12 ⇒x = 10

            i.e.,                    y  = – 9.

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44.    If 4x +  6y  = 32 and 4x – 2y = 4, then the value of 8y is :                                                           

(A) 24                                            

(B) 28

(C) 36                                            

(D) 42

Ans.     (B)

Sol.      Let      4x + 6y = 32             …… (1)

            and     4x – 2y = 4                …… (2)

            subtracting (2) from (1)   8y  = 28.

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45.    If 2x + 3y = 29 and y  = x + 3, what is the value of x ?                                                                

(A) 4                                              

(B) 5

(C) 6                                              

(D) 7

Ans.     (A)

Sol.      2x + 3 (x + 3) = 29

            ⇒    2x + 3x + 9 = 29 ⇒ 5x = 20 ⇒  x = 4.

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46.    The  solution of the two simultaneous equation 2x + y = 8 and 3y = 4 + 4x  is :                           

(A) x = 3, y = – 4                                             

(B) x = 1, y = 4

(C) x = 2,  y = 4                                               

(D) x = 4, y = 1

Ans.     (C)

Sol.      3y  = 4 + 2 ( 8 – y)

            ⇒   3y = 4 + 16 – 2y ⇒ 5y  = 20 ⇒ y = 4 then x = 2.

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47.    The solution of the simultaneous equations\frac{x}{2} + \frac{y}{3} = 4 and x + y = 10 is given by :            

(A) (– 6, 4)                                                       

(B) (6, – 4)

(C) (4, 6)                                                         

(D) (6, 4)

Ans.     (C)

Sol.      3x + 2y = 24                        …… (1)

            and    x + y = 10                  …… (2)

            In equation (1)  x + 2 (x + y)  = 24 ⇒  x + 20 = 24 ⇒ x = 4 then y = 6.

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48.    If  x + y = 6 and 3x – y = 4, then x – y is equal to :                                                                                 

(A) – 1                                           

(B) 0

(C) 2                                              

(D) 4

Ans.     (A)

Sol.      Let          x + y = 6              …… (1)

            and        3x – y = 4              …… (2)

            add (1) & (2)    4x = 10 ⇒ x =\frac{5}{2}

            and        y =6 - \frac{5}{2} =\frac{7}{2}

            i.e.,       x – y =\frac{5}{2} - \frac{7}{2} = \frac{{ - 2}}{2} =  - 1.

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49.    The solution of  2x + 3y = 2 and 3x + 2y = 2 can be represented by a point in the co-ordinate planes in : 

(A) First quadrant                                            

(B) Second quadrant                     

(C) Third quadrant                                            

(D) Fourth quadrant

Ans.     (A)

Sol.       2x + 3y = 2         …… (1)

            and          3x + 2y= 2           …… (2)

            from (1)         y =\frac{{2 - 2x}}{3}

            Now in (2)     3x + 2 \left( {\frac{{2 - 2x}}{3}} \right) = 2

          ⇒       9x + 4 – 4x = 6 ⇒ 5x  =  2 ⇒ x =\frac{2}{5}

           and     y  =\frac{{2 - \frac{4}{5}}}{3} = \frac{{10 - 4}}{{15}} = \frac{6}{{15}}

                       (x, y)  =\left( {\frac{2}{5},\frac{6}{{15}}} \right)

            i.e., In I quadrant.

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50.   The solution of the system of equations  3x – 4y = 11 and  7x + 2y = 3 is :                     

(A)  x = 1, y = 0                                               

(B) x = 0, y = – 1

(C) x = 1, y = – 2                                             

(D) x = 2, y = 1

Ans.     (C)

Sol.      3x – 4y = 11                        …… (1)

            and   7x + 2y = 3                 …… (2)

            multiplying equation (2) by 2.               

                    14x + 4y = 6

            Now adding in equation (1).

                     17x = 17 ⇒  x = 1

            and    y =\frac{{11 - 3}}{{ - 4}} = \frac{8}{{ - 4}} =  - 2.

 

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