Coordinate Geometry Practice Questions
HSC/SSC (Bangladesh) · HSC Mathematics · 143 free MCQs with instant results and detailed explanations.
143
Total
41
Easy
76
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
If the point A(2, 3) is reflected over the x-axis, what are the coordinates of the reflected point A'?
A.
(2, -3)
B.
(-2, 3)
C.
(-2, -3)
D.
(3, 2)
Show Answer & Explanation
Correct Answer: A
Reflecting a point over the x-axis involves changing the sign of the y-coordinate. Therefore, A(2, 3) becomes A'(2, -3).
Q2
Easy
What is the midpoint of the line segment joining the points (4, 2) and (10, 8)?
A.
(7, 5)
B.
(6, 6)
C.
(5, 5)
D.
(8, 4)
Show Answer & Explanation
Correct Answer: A
The midpoint M of a line segment connecting two points (x1, y1) and (x2, y2) is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2). Substituting gives M = ((4 + 10)/2, (2 + 8)/2) = (7, 5).
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, 2)
Show Answer & Explanation
Correct Answer: B
To check if a point (x, y) lies on the line, substitute x into the equation and see if y equals the result. For (0, 1), we have y = 2(0) + 1 = 1, which is true.
Q4
Medium
What is the distance between the points (3, 4) and (7, 1)?
A.
5 units
B.
4 units
C.
6 units
D.
7 units
Show Answer & Explanation
Correct Answer: A
The distance formula is √((x2 - x1)² + (y2 - y1)²). Here, x1=3, y1=4, x2=7, y2=1. Thus, distance = √((7-3)² + (1-4)²) = √(16 + 9) = √25 = 5.
Q5
Medium
Which equation represents a line parallel to the line 2x - 3y + 6 = 0 that passes through the point (2, 1)?
A.
2x - 3y - 4 = 0
B.
3x + 2y - 8 = 0
C.
2x + 3y - 7 = 0
D.
3x - 2y + 1 = 0
Show Answer & Explanation
Correct Answer: A
Lines are parallel if they have the same slope. The original line can be rearranged to find the slope, which is 2/3. So, the parallel line through (2, 1) is in the form y - 1 = (2/3)(x - 2).
Q6
Medium
What is the area of the triangle formed by the vertices (1, 1), (4, 1), and (1, 5)?
A.
6 square units
B.
8 square units
C.
10 square units
D.
4 square units
Show Answer & Explanation
Correct Answer: A
Using the formula Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| leads to Area = 1/2 |1(1-5) + 4(5-1) + 1(1-1)| = 6.
Q7
Medium
A line intersects the x-axis at (4, 0) and the y-axis at (0, 6). What is the slope of the line?
A.
-3/2
B.
3/2
C.
2/3
D.
-2/3
Show Answer & Explanation
Correct Answer: A
Slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1). Here, using points (4, 0) and (0, 6), m = (6 - 0) / (0 - 4) = 6 / -4 = -3/2.
Q8
Hard
In the coordinate plane, the line represented by the equation 3x + 4y - 12 = 0 passes through which of the following points?
A.
(4, 0)
B.
(0, 3)
C.
(2, 3)
D.
(3, 1)
Show Answer & Explanation
Correct Answer: B
To determine which point lies on the line, substitute the coordinates of each point into the equation. (0, 3) satisfies the equation as 3(0) + 4(3) - 12 = 0. The other points do not satisfy the equation.
Q9
Hard
The distance between the points A(2, 3) and B(-1, -1) in the coordinate plane is given by which of the following expressions?
A.
√[(2 - (-1))^2 + (3 - (-1))^2]
B.
√[(2 + 1)^2 + (3 + 1)^2]
C.
√[(2 - 1)^2 + (3 + 1)^2]
D.
√[(2 + 1)^2 + (3 - 1)^2]
Show Answer & Explanation
Correct Answer: A
The formula for the distance between two points (x1, y1) and (x2, y2) is √[(x2 - x1)² + (y2 - y1)²]. For A(2, 3) and B(-1, -1), this becomes √[(2 - (-1))^2 + (3 - (-1))^2].
Q10
Hard
Given the points A(2, 3), B(-1, 4), and C(3, k), find the value of k such that the area of triangle ABC is 10.
A.
5
B.
6
C.
7
D.
8
Show Answer & Explanation
Correct Answer: B
The area of triangle ABC can be calculated using the formula: Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|. Plugging in the coordinates, the area becomes 1/2 * |2(4-k) + (-1)(k-3) + 3(3-4)|. Solving for k yields k = 6.
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Coordinate Geometry — HSC/SSC (Bangladesh) HSC Mathematics Practice Questions Online
This page contains 143 practice MCQs for the chapter Coordinate Geometry in HSC/SSC (Bangladesh) HSC Mathematics. The questions are organized by difficulty — 41 easy, 76 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.