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Orienting Yourself: The Use of Coordinates – Class 9 Mathematics notes, important questions and MCQs

NCERT Class 9 Mathematics, chapter 1. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Coordinates fix the position of any point on a plane using two perpendicular number lines, the x-axis and the y-axis, meeting at the origin.

The Cartesian plane

The horizontal line is the x-axis and the vertical line is the y-axis; they meet at the origin O(0, 0).
A point is written (x, y): x = distance from the y-axis (abscissa), y = distance from the x-axis (ordinate).
(3, 5) and (5, 3) are different points — order matters.

Quadrants

Quadrant I (+, +), II (−, +), III (−, −), IV (+, −), counted anticlockwise.
Points on the x-axis have y = 0; points on the y-axis have x = 0.
Points on an axis do not belong to any quadrant.

Using coordinates

Plot points to draw shapes and read positions on maps and grids.
Horizontal or vertical distance between points = difference of the changing coordinate.
Distance between (x₁, y₁) and (x₂, y₂) = √[(x₂ − x₁)² + (y₂ − y₁)²].

Key terms

Origin: the point (0, 0) where the axes meet
Abscissa: the x-coordinate
Ordinate: the y-coordinate
Quadrant: one of the four regions made by the axes

Formulas

Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]

Important questions with answers

In which quadrant or on which axis do the points (−3, 5), (4, 0) and (−2, −7) lie?2 marks

(−3, 5) is in Quadrant II, (4, 0) lies on the x-axis, and (−2, −7) is in Quadrant III.

Plot A(2, 3), B(−2, 3) and C(−2, −1). What kind of triangle is ABC?3 marks

AB is horizontal with length 4 and BC is vertical with length 4, so ∠B = 90° and AB = BC. ABC is an isosceles right-angled triangle.

Three vertices of a rectangle are (1, 1), (5, 1) and (5, 4). Find the fourth vertex, the length of each side, the perimeter and the area.5 marks

The sides are parallel to the axes, so the fourth vertex is (1, 4). Length = 5 − 1 = 4 units, breadth = 4 − 1 = 3 units. Perimeter = 2(4 + 3) = 14 units. Area = 4 × 3 = 12 square units.

Quick revision

(x, y): x first, then y.
x-axis points (a, 0); y-axis points (0, b).
Quadrants go I → IV anticlockwise.

Exam tips

Always write the x-coordinate first.
Check signs to name the quadrant quickly.

Practice MCQs

The coordinates of the origin are
1. (0, 0)
2. (1, 1)
3. (0, 1)
4. (1, 0)
Show answer
Answer: (a) (0, 0). Both distances are zero.
The point (−4, −2) lies in quadrant
1. III
2. II
3. I
4. IV
Show answer
Answer: (a) III. Both negative.
The ordinate of (7, −3) is
1. −3
2. 7
3. 4
4. 10
Show answer
Answer: (a) −3. Ordinate = y-coordinate.
A point on the y-axis at distance 5 below the origin is
1. (5, 0)
2. (0, 5)
3. (−5, 0)
4. (0, −5)
Show answer
Answer: (d) (0, −5). x = 0, y negative.
Which point lies on the x-axis?
1. (0, 3)
2. (3, 0)
3. (3, 3)
4. (−3, 3)
Show answer
Answer: (b) (3, 0). y = 0.
The distance between (2, 3) and (2, 9) is
1. 12
2. 6
3. 3
4. 5
Show answer
Answer: (b) 6. Same x, difference of y = 6.
The points (0, 0), (4, 0) and (4, 3) form a right triangle. Its hypotenuse is
1. 4
2. 7
3. 5
4. 3
Show answer
Answer: (c) 5. √(16 + 9) = 5.
If (a, 2) lies in quadrant II, then a must be
1. positive
2. negative
3. zero
4. any number
Show answer
Answer: (b) negative. Quadrant II has negative x.

All chapters of Class 9 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.