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Coordinate Geometry Practice Questions

Class 10 · Mathematics · 1458 free MCQs with instant results and detailed explanations.

1458
Total
529
Easy
693
Medium
236
Hard

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Topics in Coordinate Geometry

Area of a Triangle 447
Distance Formula 579
Section Formula 432

Sample Questions from Coordinate Geometry

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the distance between the points (3, 4) and (6, 8) using the distance formula?
A. 5
B. 4
C. 3
D. 7
Show Answer & Explanation
Correct Answer: A
The distance formula is √((x2 - x1)² + (y2 - y1)²). Here, it calculates to √((6 - 3)² + (8 - 4)²) = √(9 + 16) = √25 = 5.
Q2
Easy
If point A is at (1, 2) and point B is at (4, 6), what is the length of line segment AB?
A. 3.6
B. 5
C. 4
D. 6
Show Answer & Explanation
Correct Answer: B
Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.
Q3
Easy
Which of the following points lies on the line segment between (0, 0) and (3, 4)?
A. (1, 2)
B. (2, 2)
C. (3, 3)
D. (4, 5)
Show Answer & Explanation
Correct Answer: A
Point (1, 2) divides the segment into two parts that maintains the ratio equivalent to the length of the segment.
Q4
Medium
What is the distance between the points (2, 3) and (5, 7) using the distance formula?
A. 5
B. 4
C. 3
D. 6
Show Answer & Explanation
Correct Answer: A
The distance can be calculated using the formula √[(x2 - x1)² + (y2 - y1)²]. Plugging in the values gives √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Q5
Medium
Which of the following points is located at a distance of 10 units from the origin?
A. (10, 0)
B. (7, 7)
C. (6, 8)
D. (4, 6)
Show Answer & Explanation
Correct Answer: A
The distance from the origin (0, 0) to a point (x, y) is calculated as √(x² + y²). For point A, √(10² + 0²) = √100 = 10.
Q6
Medium
Given points A(2, 1) and B(2, 5), what is the distance between A and B?
A. 4
B. 3
C. 2
D. 1
Show Answer & Explanation
Correct Answer: A
Since A and B have the same x-coordinate, the distance is simply the difference in their y-coordinates: |5 - 1| = 4.
Q7
Medium
What is the distance between the points (1, -1) and (4, 3)?
A. 5
B. 6
C. 4
D. 7
Show Answer & Explanation
Correct Answer: A
Using the distance formula, √[(4-1)² + (3-(-1))²] = √[(3)² + (4)²] = √[9 + 16] = √25 = 5.
Q8
Hard
Two points A(2, 3) and B(6, y) are such that the distance AB is 10 units. What is the value of y?
A. 7
B. 5
C. 1
D. 9
Show Answer & Explanation
Correct Answer: A
Using the distance formula, we set up the equation √[(6-2)² + (y-3)²] = 10, which simplifies to y = 7 after solving.
Q9
Hard
Find the distance between the points P(1, -2) and Q(-3, 4).
A. 5√2
B. 10
C. 6
D. 8
Show Answer & Explanation
Correct Answer: A
Calculating the distance using the formula gives √[(-3-1)² + (4-(-2))²] = √[16 + 36] = √52 = 5√2.
Q10
Hard
What is the distance between points A(-5, -5) and B(5, 5)?
A. 10√2
B. 15
C. 20
D. √50
Show Answer & Explanation
Correct Answer: A
Using the distance formula, d = √[(-5 - 5)² + (-5 - 5)²] = √[100 + 100] = 10√2.

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Coordinate Geometry — Class 10 Mathematics Practice Questions Online

This page contains 1458 practice MCQs for the chapter Coordinate Geometry in Class 10 Mathematics. The questions are organized by difficulty — 529 easy, 693 medium, 236 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. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.