101. A line is perpendicular to a line of slope 15. Its slope is:
- 5
- -5
- - 15
- 15
Answer: B) -5
Explanation: Perpendicular slopes multiply to -1: m2 = - 1 15 = -5. SLO M-09-B-05 · Understanding
MCQs / Mathematics / Coordinate Geometry
Coordinate Geometry MCQs — Mathematics (page 5)
195 multiple-choice questions on Coordinate Geometry from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
102. Find the distance between A(-6, -1) and B(9, -21).
- 26
- 655
- 35
- 25
Answer: D) 25
Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 15^2 + 20^2 = 625 = 25. SLO M-09-B-01 · Understanding
103. Find the distance between (-1, 4) and (4, -1).
- 10
- 3 6
- 98
- 5 2
Answer: D) 5 2
Explanation: d = 5^2 + 5^2 = 50 = 5 2. SLO M-09-B-01 · Understanding
104. The equation x5 + y-2 = 1 is written in:
- symmetric form
- normal form
- intercepts form
- slope-intercept form
Answer: C) intercepts form
Explanation: x5 + y-2 = 1 is the intercepts form. SLO M-09-B-08 · Understanding
105. The line y = -2x + 5 crosses the y-axis at:
- (5, 0)
- (0, 5)
- ( 52, 0)
- (0, -2)
Answer: B) (0, 5)
Explanation: On the y-axis x = 0, so y = 5. SLO M-09-B-04 · Knowledge
106. A school at (2, 1) and a hospital at (8, 9) want a bus stop at the midpoint of the road between them. The bus stop is at:
- (6, 8)
- (3, 4)
- (10, 10)
- (5, 5)
Answer: D) (5, 5)
Explanation: ( 2 + 82, 1 + 92 ) = (5, 5). SLO M-09-B-06 · Application
107. The lines 2x + 3y + 1 = 0 and 3x + 2y - 4 = 0 are:
- neither parallel nor perpendicular
- the same line
- perpendicular
- parallel
Answer: A) neither parallel nor perpendicular
Explanation: Slopes: m1 = - 23, m2 = - 32. They are not equal and m1 m2 = 1 neq -1. SLO M-09-B-05 · Understanding
108. The normal form of the line whose perpendicular from the origin has length 4 and makes an angle of 60^circ with the x-axis is:
- xcos 60^circ + ysin 60^circ = 4
- xcos 60^circ - ysin 60^circ = 4
- xcos 60^circ + ysin 60^circ = 16
- xsin 60^circ + ycos 60^circ = 4
Answer: A) xcos 60^circ + ysin 60^circ = 4
Explanation: Normal form: xcosalpha + ysinalpha = p. Here this is x ( 12 ) + y ( 32 ) = 4. SLO M-09-B-08 · Understanding
109. Find the gradient (slope) of the line through (1, 1) and (-7, 0).
- - 18
- 18
- 8
- -8
Answer: B) 18
Explanation: m = y2 - y1x2 - x1 = 0 - 1-7 - 1 = -1-8 = 18. SLO M-09-B-03 · Knowledge
110. The lines y = 5 and x = -2 are:
- perpendicular
- the same line
- parallel
- neither
Answer: A) perpendicular
Explanation: A horizontal line and a vertical line always meet at right angles. SLO M-09-B-05 · Understanding
111. Find the equation of the line with slope 4 passing through (-1, -6).
- y = 4x - 2
- y = 4x - 6
- y = 4x + 2
- y = -4x - 2
Answer: A) y = 4x - 2
Explanation: -6 = 4(-1) + c Rightarrow c = -2, so y = 4x - 2. SLO M-09-B-04 · Knowledge
112. The midpoint of the segment joining (0, 0) and (8, -6) is:
- (8, -6)
- (-4, 3)
- (4, -3)
- (4, 3)
Answer: C) (4, -3)
Explanation: Halve each coordinate: (4, -3). SLO M-09-B-02 · Knowledge
113. Find the distance between A(3, -4) and B(-2, -16).
- 14
- 13
- 17
- 179
Answer: B) 13
Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 5^2 + 12^2 = 169 = 13. SLO M-09-B-01 · Understanding
114. The equation of the line with slope -3 and y-intercept 1 is:
- y = -3x - 1
- y = -3x + 1
- y = 3x + 1
- y = x - 3
Answer: B) y = -3x + 1
Explanation: Put m = -3 and c = 1 into y = mx + c. SLO M-09-B-04 · Knowledge
115. Find the gradient (slope) of the line through (-3, -2) and (0, 0).
- - 23
- - 32
- 23
- 32
Answer: C) 23
Explanation: m = y2 - y1x2 - x1 = 0 - (-2)0 - (-3) = 23 = 23. SLO M-09-B-03 · Knowledge
116. The distance of the point (-9, -12) from the origin is:
- 21
- 15
- 17
- 3
Answer: B) 15
Explanation: (-9)^2 + (-12)^2 = 15. SLO M-09-B-01 · Understanding
117. A line is perpendicular to a line of slope 52. Its slope is:
- - 52
- 25
- 52
- - 25
Answer: D) - 25
Explanation: Perpendicular slopes multiply to -1: m2 = - 1 52 = - 25. SLO M-09-B-05 · Understanding
118. Islamabad is at about 33.7^circN, 73.0^circE. It lies in the:
- northern and western hemispheres
- southern and western hemispheres
- southern and eastern hemispheres
- northern and eastern hemispheres
Answer: D) northern and eastern hemispheres
Explanation: N means north of the equator; E means east of Greenwich. SLO M-09-B-07 · Application
119. On a map, latitude and longitude act like:
- two distances on a ruler
- the radius and centre of a circle
- the slope and intercept of a line
- the y- and x-coordinates of a point
Answer: D) the y- and x-coordinates of a point
Explanation: Longitude (east–west) works like x and latitude (north–south) works like y. SLO M-09-B-07 · Application
120. A hiker walks from (0, 0) to (5, 0) and then to (5, 12) (km). How far is she from her start in a straight line?
- 17 km
- 13 km
- 12 km
- 7 km
Answer: B) 13 km
Explanation: 5^2 + 12^2 = 13 km. SLO M-09-B-07 · Application
121. Find the distance between A(0, 5) and B(-12, 21).
- 21
- 20
- 28
- 2 106
Answer: B) 20
Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 12^2 + 16^2 = 400 = 20. SLO M-09-B-01 · Understanding
122. On a map grid where 1 unit = 5 km, Peshawar is at (1, -4) and Mardan is at (9, 11). The straight-line distance between them is:
- 17 km
- 170 km
- 115 km
- 85 km
Answer: D) 85 km
Explanation: Grid distance = 8^2 + 15^2 = 17 units = 17 5 = 85 km. SLO M-09-B-06 · Application
123. For the line 3x + y + 6 = 0, the slope is:
- 13
- -3
- 3
- - 13
Answer: B) -3
Explanation: m = - ab = - 31 = -3. SLO M-09-B-09 · Understanding
124. Using the two-point form, the equation of the line through (2, 1) and (6, 3) is:
- y = - 12x
- y = 12x + 1
- y = 12x
- y = 2x
Answer: C) y = 12x
Explanation: y - y1y2 - y1 = x - x1x2 - x1 gives slope 12 and y = 12x. SLO M-09-B-08 · Understanding
125. M(-6, -2) is the midpoint of AB and A = (2, 1). Find B.
- (-10, -3)
- (-14, -5)
- (-2, - 12)
- (-8, -3)
Answer: B) (-14, -5)
Explanation: x2 = 2(-6) - (2) = -14 and y2 = 2(-2) - (1) = -5, so B = (-14, -5). SLO M-09-B-02 · Knowledge
Practise Coordinate Geometry MCQs