Coordinate Geometry MCQs for Competitive Examination
Solve the following problems.
Q. 21
What would be the equation of the line, which intercepts x-axis at -5 and is perpendicular to the line y = 2x + 3?
(A) x – 2y = -5
(B) x + 2y = 5
(C) x + 2y = -5
(D) x – 2y = 5
Answer: (C) x + 2y = -5
Explanation:
Q. 22
At what point does the line 3x + 2y = -12 intercept the Y-axis?
(A) (0,6)
(B) (0,-6)
(C) (-4,0)
(D) (4,0)
Answer: (B) (0,-6)
Explanation:
Q. 23
For triangle ABC, what would be the equation of median AD if co-ordinates of A, B and C are (-5,4), (-4,0) and (-2,2) respectively?
(A) 3x – 2y = -11
(B) 3x + 2y = 7
(C) 3x + 2y = -7
(D) 3x – 2y = 11
Answer: (C) 3x + 2y = -7
Explanation:
Q. 24
The distance between the points (4,-8) and (k,0) is 10. Find k?
(A) k = 6 or -2
(B) k = 10 or -2
(C) k = 10 or -4
(D) k = 6 or -4
Answer: (B) k = 10 or -2
Explanation:
Q. 25
A line cuts the x-axis at the point (-3,0) and the y-axis at the point (0,6). What is the equation of the line?
(A) x = 2y + 6
(B) y = 2x – 6
(C) x = 2y – 6
(D) y = 2x + 6
Answer: (D) y = 2x + 6
Explanation:
Q. 26
The point Q(a, b) is first reflected in y-axis to Q1 and Q1 is reflected in the x-axis to (-6, 2). The coordinates of point Q are
(A) (-6, -2)
(B) (2, -6)
(C) (6, -2)
(D) (-2, 6)
Answer: (C) (6, -2)
Explanation:
Q. 27
The slopes of two lines are 1 and √3. What is the angle between these two lines?
(A) 15°
(B) 30°
(C) 45°
(D) 60°
Answer: (A) 15°
Explanation:
Q. 28
Reflection of the point (2, 5) in the x-axis is
(A) (2, -5)
(B) (-2, 5)
(C) (2, 5)
(D) (-2, -5)
Answer: (A) (2, -5)
Explanation:
Q. 29
What is the equation of the line passing through the point (0,4) and making an angle of 45° with the positive x axis?
(A) x + y = 4
(B) x - y = 4
(C) – x + y = 4
(D) -x - y = 4
Answer: (C) – x + y = 4
Explanation:
Q. 30
What is the slope of the line parallel to the line passing through the points (4, 6) and (2, 3)?
(A) 1/2
(B) 2
(C) 3/2
(D) -1/2
Answer: (C) 3/2
Explanation:
Q. 31
What are the co-ordinates of the centroid of a triangle, whose vertices are A(-2, 5), B(3, -2) and C(5, 3)?
(A) (-2,-2)
(B) (-2, 2)
(C) (2, 2)
(D) (2, -2)
Answer: (C) (2, 2)
Explanation: Coordinate of the centroid = ((- 2 + 3 + 5)/2, (5 – 2 + 3)/2)
Q. 32
In what ratio is the segment joining (-1, -12) and (3, 4) divided by the x-axis?
(A) 1 : 3
(B) 3 : 2
(C) 3 : 1
(D) 2 : 3
Answer: (C) 3 : 1
Explanation;
Q. 33
Point Q(-2, b) is the midpoint of segment EF. Co-ordinates of E are (-7, -6) and F are (a, 0). What is the value of a and b?
(A) a = 3; b = -3
(B) a = -3; b = -3
(C) a = 3; b = 3
(D) a = -3; b = 3
Answer: (A) a = 3; b = -3
Explanation:
Q. 34
What is the slope of the line 4x – 8y = 3?
(A) -1/2
(B) 2
(C) 1/2
(D) -2
Answer: (C) 1/2
Explanation:
Q. 35
Reflection of the point (2, -4) in the origin is
(A) (-2, 4)
(B) (-2, -4)
(C) (2, -4)
(D) (-2, 4)
Answer: (D) (-2, 4)
Explanation:
Q. 36
The line passing through the point (5, a) and point (4, 3) is perpendicular to the line x – 6y = 8. What is the value of ‘a’?
(A) -3
(B) -2
(C) 4
(D) 5
Answer: (A) – 3
Explanation:
Q. 37
The point P(3, -2) divides the segment joining the points (x, 0) and (0, y) in the ratio 1 : 3. Find x and y?
(A) x = 4; y = -8
(B)x = -3; y = -8
(C) x = 3; y = 8
(D) x = -3; y = 8
Answer: (A) x = 4; y = -8
Explanation:
Q. 38
Slope of the side DA of the rectangle ABCD is 5/3. What is the slope of the side AB?
(A) 3/5
(B) -5/3
(C) 5/3
(D) -3/5
Answer: (D) -3/5
Explanation:
Q. 39
What is the equation of the line which has 3/2 and (- 4/7) as x and y-intercept respectively?
(A) 8x – 21y = -12
(B) 8x + 21y = 14
(C) 8x – 21y = 12
(D) 8x + 21y = -14
Answer: (C) 8x – 21y = 12
Explanation:
Q. 40
What is the equation of the line if its slope is 4/3 and it passes through the point (-7, 2)?
(A) 4x – 3y = -22
(B) 4x + 3y = -34
(C) 4x + 3y = -22
(D) 4x – 3y = -34
Answer: (D) 4x – 3y = -34
Explanation: