Coordinate Geometry MCQs for Competitive Examination
Solve the following problems.
Q. 1
The area (in square units) of the triangle formed by the graphs of the equations x = 4, y = 3 and 3x + 4y = 12 is
(A) 24
(B) 12
(C) 6
(D) 3
Answer: (C) 6
Explanation:
Q. 2
The angle between the graph of the linear equation 239x − 239y + 5 = 0 and the x-axis is
(A) 0°
(B) 30°
(C) 45°
(D) 60°
Answer: (C) 45°
Explanation:
Q. 3
The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is
(A) 5
(B) 3
(C) 4
(D) 7
Answer: (A) 5
Explanation:
Q. 4
Among the equations x + 2y + 9 = 0; 5x − 4 = 0; 2y − 13 = 0; 2x − 3y = 0, the equation of the straight line passing through the origin is
(A) 2x-3y=0
(B) x+2y+9=0
(C) 5x-4=0
(D) 2y-13=0
Answer: (A) 2x-3y=0
Explanation:
Q. 5
The area of the triangle formed by the graphs of the equations x = 0, 2x + 3y = 6 and x + y = 3 is
(A) 3 square unit
(B) 4(1/2) square unit
(C) 1(1/2) square unit
(D) 1 square unit
Answer: (C) 1(1/2) square unit
Explanation:
Q. 6
The straight line y = 3x must pass through the point
(A) (0,1)
(B) (0,0)
(C) (1,2)
(D) (2,0)
Answer: (B) (0,0)
Explanation:
Q. 7
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is
(A) 6
(B) 5
(C) 4
(D) 2
Answer: (C) 4
Explanation:
Q. 8
The graph of linear equation y = x passes through the point
(A) (0, 3/2)
(B) (1,1)
(C) (-1/2, 1/2)
(D) (3/2, 3/2)
Answer: (B) (1, 1)
Explanation:
Q. 9
The graphs of x = a and y = b intersect at
(A) (a, b)
(B) (b, a)
(C) (-a, b)
(D) (a, -b)
Answer: (A) (a, a)
Explanation:
Q. 10
The graph of 2x + 1 = 0 and 3y − 9= 0 intersect at the point
(A) (-1/2, -3)
(B) (-1/2, 3)
(C) (1/2, -3)
(D) None of these
Answer: (B) (-1/2, 3)
Explanation:
Q. 11
An equation of the form ax + by + c = 0 where a ≠ 0, b ≠ 0, c = 0 represents a straight line which passes through
(A) (0, 0)
(B) (3, 2)
(C) (2, 4)
(D) None of these
Answer: (A) (0, 0)
Explanation:
Q. 12
If the graph of the equations 3x + 2y = 18 and 3y − 2x = 1 intersect at the point (p, q), then the value of p + q is
(A) 7
(B) 6
(C) 5
(D) 4
Answer: (A) 7
Explanation;
Q. 13
Find co-ordinates of the mid point of the segment joining points C (3,-5) and D (-7,3).
(A) (-2, -1)
(B) (5, -4)
(C) (-5, 4)
(D) (2, 1)
Answer: (A) (-2, -1)
Explanation:
Q. 14
A line passing through the origin perpendicularly cuts the line 2x + 3y = 6 at point M. Find M?
(A) (12/13, 18/13)
(B) (6/7, 9/7)
(C) (-6/7, 9/7)
(D) (6/11, -9/11)
Answer: (A) (12/13, 18/13)
Explanation:
Q. 15
What is the equation of the line passing through the point (2,-3) and making an angle of -45°with the positive X-axis?
(A) x – y = -5
(B) x – y = -1
(C) x + y = -5
(D) x + y = -1
Answer: (D) x + y=-1
Explanation:
Q. 16
The point P(5,-2) divides the segment joining the points (x,0) and (0,y) in the ratio 2:5. What is the value of x and y?
(A) x = -7; y = 7
(B) x = 3; y = -3
(C) x = 7; y = -7
(D) x = -3; y = 3
Answer: (C) x = 7; y = -7
Explanation:
Q. 17
What is the distance between the points (4,7) and (-1,-5)?
(A) 10 units
(B) 13 units
(C) 5 units
(D) 11 units
Answer: (B) 13 units
Explanation:
Q. 18
What will be the equation of the perpendicular bisector of segment joining the points (5,-3) and (0,2)?
(A) x + y = 2
(B) x – y = -3
(C) x + y = -2
(D) x – y = 3
Answer: (D) x – y = 3
Explanation:
Q. 19
For triangle ΔPQR, what is the equation of altitude PS if coordinates of P, Q, and R are (5,1), (0,4), and (2,3) respectively?
(A) x+2y=33
(B) 2x-y=9
(C) 2x-y=-3
(D) x+2y=-33
Answer: (B) 2x-y=9
Explanation:
Q. 20
In what ratio is the segment joining the points (2,5) and (6,10) divided by the y axis?
(A) 3 : 1
(B) 1 : 3
(C) 2 : 5
(D) 5 : 2
Answer: (B) 1 : 3
Explanation: