x y A(x₁,y₁) B(x₂,y₂) C(x₃,y₃) mid m:n d=√(Δx²+Δy²) Collinear ⟺ Area=0
(x,y)
Chapter 7  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Coordinate Geometry

Three Formulae, Maximum Marks — Distance, Section, Area at Speed

📋 50 MCQs ⭐ 30 PYQs ⏱ 65 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
20Medium
10Hard
30PYQs
65 secAvg Time/Q
6Topics
Easy 40% Medium 40% Hard 20%

Why Practise These MCQs?

CBSE Class XNTSEState Boards

Coordinate Geometry is the most formula-mechanical chapter in Class X — three formulae cover the entire chapter. CBSE Boards deliver 8–10 marks annually from distance formula, section formula, and area of triangle. "Classify the quadrilateral" problems (rhombus, square, parallelogram) are 4-mark CBSE staples. Collinearity via zero area is a quick 1-marker every exam.

Topic-wise MCQ Breakdown

Distance Formula12 Q
Section Formula (Internal Division)10 Q
Section Formula (External Division)3 Q
Midpoint Formula6 Q
Area of Triangle (Coordinate Method)10 Q
Collinearity (Zero Area Test)5 Q
Centroid & Special Points4 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$PQ = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$\text{Section (m:n): }\left(\tfrac{mx_2+nx_1}{m+n},\ \tfrac{my_2+ny_1}{m+n}\right)$
$\text{Midpoint: }\left(\tfrac{x_1+x_2}{2},\ \tfrac{y_1+y_2}{2}\right)$
$\text{Area} = \tfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$
$\text{Collinear} \Leftrightarrow \text{Area} = 0$

MCQ Solving Strategy

Distance formula: expand (x₂−x₁)² and (y₂−y₁)² separately before adding — avoids sign errors. Section formula: label which point is (x₁,y₁) and which is (x₂,y₂) consistently. For "classify quadrilateral" problems: compute all 4 sides and both diagonals — the combination tells you the shape. Area formula: use the cyclic (shoelace) pattern — go clockwise or anticlockwise consistently.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Distance between two points, midpoint, identify collinear points

② Medium

Section formula, centroid, area of triangle from coordinates

③ Hard

Classify quadrilateral (all 4 sides + diagonals), external division

★ PYQ

CBSE — section formula + area combo; NTSE — coordinate geometry logic

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Introduction to Trigonometry
🎯 Knowledge Check

Maths — Coordinate Geometry

50 Questions Class 10 MCQs
1
What are the coordinates of the origin?
2
A point with coordinates (3, -5) lies in which quadrant?
3
The distance between the points (0,0) and (6,8) is:
4
For points \((x_1, y_1)\) and \((x_2, y_2)\), the distance formula is:
5
The midpoint of the segment joining (4, 6) and (2, 10) is:
6
The point (0, y) always lies on the:
7
Distance between (1,2) and (1,8) is:
8
A point equidistant from (2, 3) and (2, -1) must lie on:
9
The coordinates of a point dividing the segment between (-4, 2) and (6, 8) in ratio 1:1 is:
10
If the distance between two points is zero, they are:
11
Distance of point (7, 24) from origin is:
12
Which of the following lies in Quadrant II?
13
Midpoint of (0, 0) and (8, 4) is:
14
The distance between (-3, 4) and (3, 4) is:
15
The abscissa of point (6, -2) is:
16
The ordinate of (-7, 12) is:
17
A point on x-axis has coordinates:
18
What is the distance between (5, 9) and (5, 9)?
19
Section formula divides a segment in ratio:
20
Midpoint of (a, b) and (c, d) is:
21
The point (3, 0) lies on:
22
Which point has both coordinates negative?
23
Distance between (0, 5) and (12, 5) is:
24
The point dividing (2, 2) & (10, 6) in ratio 1:3 is:
25
In the distance formula, squaring ensures:
26
What is the distance between (-4, -3) and (-4, 5)?
27
The point (0, -3) is on:
28
Which point lies in Quadrant I?
29
Distance between (3, 4) and (0, 0) is:
30
Midpoint of (6, -2) and (10, -6) is:
31
If a point lies in Quadrant III, its coordinates satisfy:
32
A point on y-axis must have:
33
The distance between (a, b) and (a, d) is:
34
Which is NOT true about a midpoint?
35
The coordinates of a point are (x, y). Here x is:
36
Distance between (1, 7) and (9, 7) is:
37
The point (-5, 0) belongs to:
38
Coordinates dividing (4, 6) and (8, 10) in 1:1 ratio:
39
Distance between (-2, -3) and (2, 3) is:
40
The distance of \((x, y)\) from origin is:
41
Which is true for Quadrant IV?
42
Distance between (-1, 4) and (3, 4) is:
43
Midpoint of (-2, -2) & (6, 6):
44
A point dividing a segment externally uses:
45
Which point lies on line x = 5?
46
Distance between (0, 0) and \((x, 0)\):
47
Coordinates dividing (3, 3) and (9, 9) in ratio 1:2:
48
A point (a, 0) lies in:
49
A point (0, b) lies in:
50
The distance between \((x_1, y_1)\) and \((x_1, y_2)\) depends only on:
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Coordinate Geometry Class 10 MCQs (50 Qs) – NCERT Ch 7
Coordinate Geometry Class 10 MCQs (50 Qs) – NCERT Ch 7 — Complete Notes & Solutions · academia-aeternum.com
Mastering Coordinate Geometry becomes easier and more engaging when learners test their understanding through well-structured Multiple Choice Questions (MCQs). This collection of MCQs for Chapter 7 is designed to strengthen conceptual clarity, sharpen analytical thinking, and build exam-ready confidence for Class 10 students. Each question targets essential ideas such as plotting points, identifying quadrants, calculating distances, finding midpoints, applying the section formula, and…
🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Frequently Asked Questions

Coordinate Geometry (Analytical Geometry) is the branch of mathematics that represents points, lines, and shapes using numerical coordinates on a plane.

The Cartesian plane is a two-dimensional plane formed by two perpendicular number lines: the x-axis and the y-axis.

Coordinates are ordered pairs (x, y) that represent the position of a point on the Cartesian plane.

The x-axis is the horizontal axis on the coordinate plane.

The y-axis is the vertical axis on the coordinate plane.

The origin (0, 0) is the point where the x-axis and y-axis intersect.

Abscissa is the x-coordinate of a point.

Ordinate is the y-coordinate of a point.

The plane is divided into four quadrants numbered counterclockwise starting from the top-right region.

Quadrant I (+,+), Quadrant II (-,+), Quadrant III (-,-), Quadrant IV (+,-).

\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

To find the distance between two points on the coordinate plane.

\( M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \).

It finds the exact center between two given points.

For a point dividing line segment in ratio m:n internally: ( P = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right) ).

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    Coordinate Geometry – Learning Resources

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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Coordinate Geometry Class 10 MCQs (50 Qs) – NCERT Ch 7
    Coordinate Geometry Class 10 MCQs (50 Qs) – NCERT Ch 7 — Complete Notes & Solutions · academia-aeternum.com
    Mastering Coordinate Geometry becomes easier and more engaging when learners test their understanding through well-structured Multiple Choice Questions (MCQs). This collection of MCQs for Chapter 7 is designed to strengthen conceptual clarity, sharpen analytical thinking, and build exam-ready confidence for Class 10 students. Each question targets essential ideas such as plotting points, identifying quadrants, calculating distances, finding midpoints, applying the section formula, and…
    🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
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    X / Twitter
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    Threads
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    Email
    academia-aeternum.com/class-10/mathematics/coordinate-geometry/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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