Are these practice questions for Coordinate Geometry based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Coordinate Geometry free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Coordinate Geometry mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Coordinate Geometry for full coverage.

How many practice questions are there for Coordinate Geometry?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Coordinate Geometry Class 10 Mathematics Practice Questions with Answers

easy

What are the coordinates of a point on the x-axis? Explain why the y-coordinate is zero for any point on the x-axis.

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easy

Identify the quadrant in which the following points lie and state the sign of their abscissa and ordinate: (a)

(2, 5)

, (b)

(-3, 1)

, (c)

(-4, -6)

.

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easy

Write the coordinates of a point that lies on the y-axis at a distance of 5 units from the origin in the positive direction.

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easy

State the mid-point formula for a line segment joining the points

A(x_1, y_1)

and

B(x_2, y_2)

.

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easy

Solve for the coordinates of the point which divides the line segment joining A(-1, 7) and B(4, -3) in the ratio 2:3.

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easy

Explain the condition for three points

A, B,

and

C

to be collinear using the distance formula.

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easy

Evaluate the statement: "The midpoint formula is a special case of the section formula." Justify your reasoning.

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easy

Propose a method using the distance formula to determine if a point

P(x, y)

lies inside, outside, or on a circle with center

C(h, k)

and radius

r

.

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easy

State the formula to find the distance between two points

P(x_1, y_1)

and

Q(x_2, y_2)

.

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easy

Calculate the distance between the points A(2, -3) and B(10, -9).

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easy

Define the term 'ordinate' of a point.

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easy

Create a problem where the coordinates of a point

P

that divides a line segment

AB

in a given ratio are known, and you need to find the coordinates of an endpoint

B

, given endpoint

A

. Solve the problem for

A = (1, 5)

,

P = (4, -1)

, and the ratio

AP:PB = 3:2

.

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easy

Calculate the distance of the point C(-8, 15) from the origin O(0, 0).

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medium

Summarize the steps to prove that four given points

A, B, C,

and

D

form a parallelogram but not a rectangle, using the distance formula.

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medium

Propose a coordinate-based method and find the coordinates of the circumcenter of a right-angled triangle whose vertices are

O(0,0)

,

A(2a, 0)

, and

B(0, 2b)

.

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medium

State the formula for the distance of a point

P(x, y)

from the origin

O(0, 0)

.

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medium

Explain how the mid-point formula is a special case of the section formula.

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medium

List the conditions that must be satisfied for four points

A, B, C,

and

D

to be the vertices of a rhombus, using the distance formula.

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medium

State the section formula and explain what each variable represents.

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medium

The vertices of a triangle are A(1, k), B(4, -3) and C(-9, 7). If its centroid is G(1, 4), calculate the value of k.

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medium

Describe how you would use the distance formula to determine if a triangle with given vertices

A, B,

and

C

is an isosceles triangle.

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medium

Find the point on the y-axis which is equidistant from the points M(5, -2) and N(-3, 2).

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medium

Explain the concept of 'trisection' of a line segment. Describe how to find the coordinates of the points of trisection for a line segment joining

A(x_1, y_1)

and

B(x_2, y_2)

using the section formula.

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medium

A line segment joining

A(2, -2)

and

B(11, 7)

is divided by a point

P(x, 4)

. Justify the ratio in which

P

divides the line segment

AB

, and then find the x-coordinate of

P

.

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medium

Show that the points A(-2, -1), B(1, 0), C(4, 3), and D(1, 2) are the vertices of a parallelogram. Is it a rectangle? Examine and justify.

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medium

Derive the formula for the coordinates of the centroid of a triangle with vertices

A(x_1, y_1)

,

B(x_2, y_2)

, and

C(x_3, y_3)

. (Hint: The centroid divides each median in the ratio 2:1).

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medium

Formulate the conditions, using the distance formula, for four points

A, B, C, D

taken in order, to be the vertices of a rhombus but not a square.

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medium

Prove, using coordinate geometry, that the diagonals of a rectangle are equal in length and bisect each other.

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medium

Examine if the points A(1, 1), B(3, 2), and C(7, 4) are collinear.

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medium

A point P lies on the x-axis. If its distance from the point A(0, -4) is 5 units, calculate the possible coordinates of P.

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medium

If A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram taken in order, demonstrate the property of its diagonals to find the value of p.

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medium

Formulate the linear equation that represents the locus of all points

(x, y)

that are equidistant from the points

A(-1, 4)

and

B(5, -2)

. Interpret the geometric meaning of this equation.

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medium

Describe the derivation of the distance formula,

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

, for two points

P(x_1, y_1)

and

Q(x_2, y_2)

. Use a brief explanation of the geometric construction.

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medium

Determine the ratio in which the point P(2, y) divides the line segment joining the points A(-2, 2) and B(3, 7). Also, solve for the value of y.

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medium

Analyze if the points P(3, 4), Q(-2, 3), and R(5, -6) form an isosceles triangle.

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medium

A student claims that for three distinct points A, B, and C, if they are collinear, then it must be that

AB + BC = AC

. Justify whether this claim is always true for any arrangement of the collinear points.

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hard

The vertices of a triangle are A(5, 1), B(-3, -7), and C(7, -1). Calculate the length of the median through vertex A and find the coordinates of the centroid.

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hard

Design a solution for the following problem: Two ancient wells are located at positions

W_1(-4, 2)

and

W_2(2, 8)

on a village map. A straight irrigation canal is to be built such that every point on the canal is equidistant from both wells.

Formulate the linear equation of the path of the canal.
If the canal intersects a straight road represented by the y-axis, find the coordinates of the intersection point.
Justify why this canal is the perpendicular bisector of the line segment joining the two wells.

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hard

Determine the ratio in which the line

x - 3y = 0

divides the line segment joining the points A(-2, -5) and B(6, 3). Also, find the coordinates of the point of intersection.

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hard

Let

P, Q, R, S

be the midpoints of the sides

AB, BC, CD, DA

respectively of an arbitrary quadrilateral

ABCD

. Justify, using coordinate geometry, that

PQRS

is a parallelogram.

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hard

Evaluate the type of triangle formed by the vertices

A(a, a)

,

B(-a, -a)

, and

C(-a\sqrt{3}, a\sqrt{3})

for

a \neq 0

. Justify your answer with calculations.

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hard

Critique the following reasoning: "To find a point on the y-axis equidistant from

A(x_1, y_1)

and

B(x_2, y_2)

, I must find the midpoint of AB."

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hard

Create a proof using coordinate geometry to show that the medians to the equal sides of an isosceles triangle are equal in length. (Hint: Place the vertices strategically on the coordinate axes, for example, at

A(0, a)

,

B(-b, 0)

, and

C(b, 0)

).

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hard

Solve for the coordinates of the points that trisect the line segment joining P(4, -1) and Q(-2, -3).

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Coordinate GeometryClass 10 Mathematics Practice Questions