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Coordinate Geometry — Class 10 MCQs with Answers

Class 10 CBSE Mathematics · Chapter 7

108 practice questions · 31 Easy · 39 Medium · 38 Hard · Updated

Jump to the 6 solved questions

Practise the most important Class 10 CBSE Mathematics questions from Chapter 7, "Coordinate Geometry". You get 11 timed quizzes made from 108 NCERT-based MCQs, with answers and explanations. The questions are split into 31 Easy, 39 Medium and 38 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.

To score well in "Coordinate Geometry", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.

Use this chapter for focused revision. Start with the Easy set to check your basics on Coordinate Geometry, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.

Coordinate Geometry — important questions & MCQs with answers (Class 10 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

  1. Q1 of 6Easy

    Distance between (0,0) and (3,4) is:

    A coordinate grid with the x-axis and y-axis marked and numbered. Two points are plotted, labelled (0, 0) and (3, 4), joined by a straight segment.

    Show answer

    Answer: 5

    Explanation: Distance formula √[(x₂−x₁)²+(y₂−y₁)²]: √[(3−0)²+(4−0)²] = √(9+16) = √25 = 5 units.

  2. Q2 of 6Easy

    Midpoint of (2,3) and (4,7) is:

    A coordinate grid with the x-axis and y-axis marked and numbered. Two points are plotted, labelled (2, 3) and (4, 7), joined by a straight segment.

    Show answer

    Answer: (3,5)

    Explanation: Midpoint formula ((x₁+x₂)/2, (y₁+y₂)/2): ((2+4)/2, (3+7)/2) = (3, 5).

  3. Q3 of 6Medium

    If the distance between (a, 0) and (0, 4) is 5, then the possible values of a are:

    A coordinate grid with the x-axis and y-axis marked and numbered. A point is plotted, labelled (0, 4).

    Show answer

    Answer: 3 and −3

    Explanation: Distance formula: √(a² + 4²) = 5 ⇒ a² + 16 = 25 ⇒ a² = 9 ⇒ a = ±3. Squaring loses the sign, so both roots are valid — picking only +3 misses one answer.

  4. Q4 of 6Medium

    Assertion (A): The point that divides the line segment joining (1, 2) and (7, 8) internally in the ratio 1 : 2 is (3, 4). Reason (R): The distance between two points is always non-negative.

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    Answer: Both A and R are true but R is not the correct explanation of A

    Explanation: A is true: x = (1 × 7 + 2 × 1)/3 = 3 and y = (1 × 8 + 2 × 2)/3 = 4. R is also true, but A comes from the section formula, not from R.

  5. Q5 of 6Hard

    If A(6, 1), B(8, 2), C(9, 4), D(p, 3) are vertices of a parallelogram taken in order, then p equals:

    A coordinate grid with the x-axis and y-axis marked and numbered. Three points are plotted, labelled A(6, 1), B(8, 2) and C(9, 4). These are three vertices of parallelogram ABCD; the fourth vertex D is not drawn.

    Show answer

    Answer: 7

    Explanation: In parallelogram ABCD, midpoint of AC = midpoint of BD. Midpoint AC = ((6+9)/2, (1+4)/2) = (7.5, 2.5). Midpoint BD = ((8+p)/2, (2+3)/2) = ((8+p)/2, 2.5). Equate x: (8+p)/2 = 7.5 ⇒ p = 7.

  6. Q6 of 6Hard

    Assertion (A): The points A(2, 1), B(4, 3) and C(7, 6) are collinear. Reason (R): A point that is equidistant from two points A and B lies on the perpendicular bisector of AB.

    Show answer

    Answer: Both A and R are true but R is not the correct explanation of A

    Explanation: A is true: AB = 2√2, BC = 3√2 and AC = 5√2, so AB + BC = AC. R is also true, but it is about equidistant points and does not explain why A, B and C lie on a line.

Coordinate Geometry notes: key concepts (Class 10 Mathematics)

Placing a figure on the coordinate plane turns geometric questions into arithmetic. This chapter finds the distance between two points, the point dividing a segment in a given ratio, and the area of a triangle from its vertices alone.

Distance formula
The straight-line distance between two points, obtained by applying Pythagoras to the horizontal and vertical gaps.
Axes x and y with two points A(x₁, y₁) and B(x₂, y₂) joined by a straight segment marked d. A right triangle is drawn under it: the horizontal side from A is x₂ − x₁ and the vertical side up to B is y₂ − y₁, with the right angle at the corner. By Pythagoras, d² = (x₂ − x₁)² + (y₂ − y₁)².
Distance from the origin
A special case of the distance formula, √(x² + y²), used constantly in shorter problems.
Section formula (internal)
The coordinates of the point dividing the segment joining two points internally in the ratio m : n.
Axes x and y with a segment from A(x₁, y₁) to B(x₂, y₂). A point P(x, y) on it divides it internally: the part AP is marked m and the part PB is marked n, so AP : PB = m : n. Below: x = (mx₂ + nx₁)/(m + n) and y = (my₂ + ny₁)/(m + n).
Midpoint formula
The section formula with ratio 1 : 1 — simply the averages of the two endpoints' coordinates.
Ratio in which a point divides a segment
Given the dividing point, the ratio can be recovered by setting up the section formula and solving for m : n.
Point of division on an axis
A point on the x-axis has y = 0, which turns the section formula into a single equation for the unknown ratio.
Area of a triangle from vertices
A determinant-style formula giving the area directly from the three vertices, with no need for a base or height.
Collinearity test
Three points are collinear exactly when the triangle they form has zero area — the quickest algebraic check.
Centroid of a triangle
The point where the medians meet, whose coordinates are the averages of the three vertices' coordinates.
Triangle with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃). Each vertex is joined to the midpoint of the opposite side (D on BC, E on CA, F on AB); the equal halves of each side carry matching ticks. The three medians AD, BE and CF meet at one point G, the centroid. Below: G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3).
Identifying quadrilaterals
Compute all four sides and both diagonals: equal sides and equal diagonals distinguish a square, rectangle, rhombus or parallelogram.
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Coordinate Geometry — FAQs

What are the key concepts in Class 10 Mathematics Coordinate Geometry?+

Placing a figure on the coordinate plane turns geometric questions into arithmetic. This chapter finds the distance between two points, the point dividing a segment in a given ratio, and the area of a triangle from its vertices alone. Key ideas include Distance formula, Distance from the origin, Section formula (internal), Midpoint formula, Ratio in which a point divides a segment, Point of division on an axis.

What does Class 10 Mathematics Chapter 7 (Coordinate Geometry) cover on XamBaaz?+

It has 108 NCERT-based MCQs on "Coordinate Geometry": 31 Easy, 39 Medium and 38 Hard. Together they make 11 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.

Are these "Coordinate Geometry" questions free to practise?+

Yes. Sign in with Google to practise "Coordinate Geometry" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 10 till 31 March; on 1 April your account moves up to Class 11 and the rest of your year carries over. No chapter is charged separately.

How should I revise "Coordinate Geometry" for the exam?+

Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 11 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.

Are these "Coordinate Geometry" MCQs available with answers?+

Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.

Is there negative marking in the "Coordinate Geometry" quizzes?+

Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.

What are the important questions from Coordinate Geometry (Class 10 Mathematics)?+

The questions that matter most test Distance formula, Distance from the origin, Section formula (internal), Midpoint formula, Ratio in which a point divides a segment, Point of division on an axis. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 108 questions on the chapter as timed quizzes.

Is there an online quiz for Coordinate Geometry?+

Yes — Class 10 Mathematics Coordinate Geometry has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.

Are there question answers and extra questions for Coordinate Geometry (Class 10 Mathematics)?+

Yes. This page has 6 solved questions on Coordinate Geometry, each with the correct answer and a short explanation. Sign in to practise all 108 questions on the chapter as timed quizzes.

Are there assertion–reason and case study questions for Coordinate Geometry (Class 10 Mathematics)?+

Yes. The Coordinate Geometry question bank has 6 assertion–reason questions and 12 case-based (case study) questions in the CBSE board format, alongside the regular MCQs. Each comes with the answer and a worked explanation. Sign in to practise them in timed quizzes.

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