Are these practice questions for Orienting Yourself: The Use of Coordinates based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 9 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Orienting Yourself: The Use of Coordinates free?

Yes. Every chapter includes free practice questions for Class 9 students to get you started.

What types of questions are included?

The practice set for Orienting Yourself: The Use of Coordinates 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 Orienting Yourself: The Use of Coordinates for full coverage.

How many practice questions are there for Orienting Yourself: The Use of Coordinates?

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

Orienting Yourself: The Use of Coordinates Class 9 Mathematics Practice Questions with Answers

easy

Identify the x-coordinate and the y-coordinate of the point P(-8, 3).

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easy

Summarize the key components of a Cartesian coordinate system. Include descriptions of the axes, the origin, the quadrants, and how a point is located.

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easy

What is the name given to the vertical line in the Cartesian plane?

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easy

Identify the quadrant or axis on which each of the following points lie: A(2, 5), B(-3, 1), C(7, -4), D(0, -6).

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easy

Analyze the point

P(-4, 9)

. In which quadrant does it lie and what is its perpendicular distance from the x-axis?

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easy

A point lies on the y-axis at a distance of 6 units below the origin. Another point lies on the x-axis at a distance of 10 units to the left of the origin. Write the coordinates of both points.

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easy

Justify why a two-dimensional floor plan of a room, represented on a Cartesian plane, is insufficient to specify the location of a wall clock.

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easy

Define the 'origin' in a Cartesian coordinate system.

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easy

Critique the statement: 'A point with coordinates

(0, k)

where

k

is any real number can lie in either Quadrant I or Quadrant IV.' Justify your answer.

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easy

Calculate the perimeter of the triangle with vertices

P(0, 4)

,

Q(0, 0)

, and

R(3, 0)

.

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medium

Derive the formula for the coordinates of the midpoint

M(x, y)

of a line segment joining points

P(x_1, y_1)

and

Q(x_2, y_2)

. Justify your steps using geometric constructions and properties of similar triangles.

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medium

Explain the sign conventions for the x and y coordinates in all four quadrants of the Cartesian plane. You may use a simple diagram to illustrate your explanation.

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medium

Examine if the points

A(1, 5)

,

B(2, 3)

, and

C(-2, -11)

are collinear.

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medium

State the formula for calculating the distance between two points, P(

x_1, y_1

) and Q(

x_2, y_2

), in a Cartesian plane.

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medium

Examine if the points

A(1, 1)

,

B(5, 3)

,

C(3, 7)

, and

D(-1, 5)

are the vertices of a rhombus.

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medium

If the distance of a point

P(x, 4)

from the origin is 5 units, calculate the possible values of

x

.

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medium

A triangular park is defined by the vertices

A(-3, 0)

,

B(3, 0)

, and

C(0, 4)

. Calculate the area of this park. (Assume coordinates are in kilometers).

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medium

List the sign convention for the coordinates (x, y) in the third quadrant.

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medium

A map is laid out on a coordinate grid. A fountain is at

F(2, 1)

, a bench is at

B(2, 7)

, and a lamppost is at

L(6, 1)

. A straight path connects the bench to the lamppost. Calculate the length of this path.

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medium

Analyze if the point

P(4, 5)

lies inside, on, or outside the circle with its center at the origin

O(0, 0)

and a radius of 6 units.

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medium

Describe the process of plotting a point P(x, y) on a Cartesian plane. Use the point Q(-4, 6) as an example, explaining each step and identifying the quadrant.

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medium

Propose a condition on the coordinates

(a, b)

of a point

P

such that it is equidistant from the x-axis and the y-axis. Justify your condition.

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medium

Calculate the coordinates of a point on the x-axis which is equidistant from the points

A(2, -5)

and

B(-2, 9)

.

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medium

Formulate a general rule to find the coordinates of the fourth vertex

D(x, y)

of a rectangle

ABCD

, given the coordinates of three consecutive vertices

A(x_1, y_1)

,

B(x_2, y_2)

, and

C(x_3, y_3)

. Justify your rule.

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medium

Critique the concept of a coordinate system that uses only positive numbers and zero. Would it be possible to map every point in a plane using such a system? Justify your reasoning.

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medium

Describe the location of a point P(x, y) if: (i) x = 0 and y > 0 (ii) x < 0 and y = 0 (iii) x < 0 and y < 0

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medium

What is the general form of the coordinates for any point lying on the x-axis?

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medium

Calculate the coordinates of the mirror image of the point

Q(5, -8)

when reflected across the y-axis.

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medium

Three vertices of a rectangle

ABCD

are

A(2, 2)

,

B(8, 2)

, and

C(8, 6)

. Plot these points on a graph and determine the coordinates of the fourth vertex

D

. Also, calculate the length of the diagonal

AC

.

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medium

A circle is centered at the origin

O(0, 0)

and passes through the point

P(6, -8)

. Evaluate whether the point

Q(7, 7)

lies inside the circle, on the circle, or outside the circle. Justify your answer with calculations.

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medium

Design a test using the distance formula to evaluate whether a triangle with vertices

A(x_1, y_1)

,

B(x_2, y_2)

, and

C(x_3, y_3)

is a right-angled triangle. Apply your test to the points

A(1, 1)

,

B(5, 3)

, and

C(4, 5)

.

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medium

Explain the difference between the coordinates (a, b) and (b, a) when a is not equal to b. Provide an example.

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medium

A point

R

has a y-coordinate of -3. Can you predict the coordinates of point

S

which is on the line through

R

parallel to the x-axis? Which quadrants can

S

lie in?

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hard

A city park is laid out on a coordinate grid. The park entrance is at the origin

E(0, 0)

. An ancient oak tree is at

O(12, 5)

and a fountain is at

F(4, -10)

. A straight path connects the entrance to the oak tree. Another straight path connects the oak tree to the fountain. A visitor walks from the entrance to the oak tree, and then to the fountain. Create a third point,

P

, on the path

EF

such that the total distance walked by the visitor (

EO + OF

) is minimized. Justify why the path

E \to O \to F

is not the shortest path from the entrance to the fountain, and calculate how much shorter the direct path

EF

is.

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hard

Propose coordinates for the four vertices of an isosceles trapezoid that is symmetric with respect to the y-axis, has a height of 5 units, a top base of length 6 units, and a bottom base of length 10 units. Justify your choice of coordinates.

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hard

A point is 5 units away from the x-axis and 3 units away from the y-axis, and it lies in the second quadrant. Identify its coordinates.

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hard

Propose and justify a method to find the coordinates of the circumcenter of a right-angled triangle with vertices

A(x_1, y_1)

,

B(x_2, y_2)

, and

C(x_3, y_3)

, where the right angle is at vertex B. Apply your method to find the circumcenter of the triangle with vertices

A(1, 5)

,

B(1, 1)

, and

C(4, 1)

.

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hard

Justify that the points

A(-4, -5)

,

B(0, -3)

, and

C(8, 1)

are collinear by using the distance formula.

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hard

A student claims that any three distinct points

A(2, 3)

,

B(5, 3)

, and

C(5, 7)

will always form a right-angled triangle. Evaluate this claim and justify your conclusion.

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hard

Design the coordinates for the vertices of a square

PQRS

of side length

10

units, such that its diagonals lie on the x and y axes. Justify that your created shape is a square.

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hard

Recall the historical contribution of René Descartes to coordinate geometry as mentioned in the source text.

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hard

Plot the points

A(4,0)

and

B(-4,0)

. If

C

is a point such that

\triangle ABC

is an equilateral triangle, analyze and find the possible coordinates of point

C

.

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hard

Based on the source text, list and briefly describe the contributions of three different historical figures or civilizations to the development of coordinate systems.

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hard

Analyze the triangle formed by the points

P(5, -2)

,

Q(1, -2)

, and

R(5, 3)

. Determine what kind of triangle it is (scalene, isosceles, or equilateral) and calculate its area.

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Orienting Yourself: The Use of CoordinatesClass 9 Mathematics Practice Questions