Coordinate Geometry Practice Questions
IGCSE (Cambridge) · IGCSE Mathematics · 141 free MCQs with instant results and detailed explanations.
141
Total
47
Easy
68
Medium
26
Hard
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Sample Questions from Coordinate Geometry
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?
A.
(3, 5)
B.
(2, 5)
C.
(4, 7)
D.
(6, 10)
Show Answer & Explanation
Correct Answer: A
The midpoint formula is ( (x1 + x2)/2 , (y1 + y2)/2 ). For points (2, 3) and (4, 7), the midpoint is ((2 + 4)/2, (3 + 7)/2) = (3, 5).
Q2
Easy
Which of the following points lies on the line represented by the equation y = 2x + 1?
A.
(1, 3)
B.
(2, 5)
C.
(0, 1)
D.
(3, 4)
Show Answer & Explanation
Correct Answer: C
To check if a point lies on the line y = 2x + 1, substitute the x-coordinate into the equation. For (0, 1), y = 2(0) + 1 = 1, which matches the y-coordinate.
Q3
Easy
Which of the following points lies on the line represented by the equation y = 2x + 1?
A.
(1, 3)
B.
(0, 1)
C.
(2, 5)
D.
(3, 10)
Show Answer & Explanation
Correct Answer: B
To determine if a point lies on the line y = 2x + 1, we substitute the x-coordinate of the point into the equation. For point (0, 1), substituting x = 0 gives y = 2(0) + 1 = 1, which matches the y-coordinate. Hence, this point lies on the line.
Q4
Medium
If the midpoint of the line segment joining points A(2, 3) and B(x, 5) is M(4, 4), what is the value of x?
A.
6
B.
8
C.
10
D.
5
Show Answer & Explanation
Correct Answer: B
The midpoint M of points A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2). For M(4, 4), we set up the equations: (2 + x)/2 = 4 and (3 + 5)/2 = 4. Solving (2 + x)/2 = 4 gives x = 8.
Q5
Medium
What is the gradient (slope) of the line that passes through the points (1, 2) and (4, 8)?
A.
2
B.
3
C.
1.5
D.
2.5
Show Answer & Explanation
Correct Answer: A
The gradient m of a line through points (x1, y1) and (x2, y2) is calculated as m = (y2 - y1) / (x2 - x1). Here, m = (8 - 2) / (4 - 1) = 6 / 3 = 2.
Q6
Medium
If the midpoint of the line segment connecting points A(2, 3) and B(x, 7) is M(5, 5), what is the value of x?
A.
8
B.
6
C.
4
D.
10
Show Answer & Explanation
Correct Answer: A
The midpoint M is given by ((x1 + x2)/2, (y1 + y2)/2). Here, (2 + x)/2 = 5 and (3 + 7)/2 = 5. Solving (2 + x)/2 = 5 gives x = 8.
Q7
Medium
Which of the following equations represents a vertical line passing through the point (4, -2)?
A.
x = 4
B.
y = -2
C.
y = 4
D.
x + y = 2
Show Answer & Explanation
Correct Answer: A
A vertical line has a constant x-coordinate. The equation x = 4 indicates all points where x is always 4, which corresponds to the vertical line through (4, -2).
Q8
Hard
Given the points A(2, 3) and B(8, 7), find the equation of the line passing through both points in the form y = mx + c.
A.
y = (2/3)x + 1
B.
y = (2/3)x + 5/3
C.
y = (2/3)x + 3
D.
y = (2/3)x + 6
Show Answer & Explanation
Correct Answer: C
The slope (m) between points A and B is calculated as (7-3)/(8-2) = 2/3. Using point A (2, 3) in the equation y - y1 = m(x - x1) gives y - 3 = (2/3)(x - 2). Simplifying yields y = (2/3)x + 3.
Q9
Hard
Which of the following points lies on the line represented by the equation 3x - 4y + 12 = 0?
A.
(2, 0)
B.
(0, -3)
C.
(4, 3)
D.
(1, 3)
Show Answer & Explanation
Correct Answer: B
To determine which point lies on the line, substitute the coordinates of each option into the equation. For (0, -3): 3(0) - 4(-3) + 12 = 0, which simplifies to 0 = 0, confirming it lies on the line.
Q10
Hard
A point P lies on the line defined by the equation y = 2x + 3. If the x-coordinate of P is -2, what is the y-coordinate of P?
A.
1
B.
3
C.
-1
D.
-5
Show Answer & Explanation
Correct Answer: C
Substituting the x-coordinate (-2) into the equation y = 2(-2) + 3 results in y = -4 + 3 = -1. Thus, the correct y-coordinate is -1.
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Coordinate Geometry — IGCSE (Cambridge) IGCSE Mathematics Practice Questions Online
This page contains 141 practice MCQs for the chapter Coordinate Geometry in IGCSE (Cambridge) IGCSE Mathematics. The questions are organized by difficulty — 47 easy, 68 medium, 26 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.