# Find the coordinates of a point

In this chapter we will learn to find the location of coordinates of a given point.

## Coordinates of the point

Follow the below steps to identify the location of given point.

(a) Perpendicular line to x axis

Draw imaginary perpendicular line from given point to x axis.

The marking on x axis will tell you the horizontal distance from origin. Hence, it gives you the value of x coordinate of given point.

(b) Perpendicular line to y axis

Draw imaginary perpendicular line from given point to y axis.

The marking on y axis will tell you the vertical distance from origin. Hence, it is y coordinate of a given point.

(c) Forming ordered pair

Write the values of x & y coordinate in the form of ordered pair.

The location of given point is written as ⟹ (x coordinate, y coordinate )

I hope you understood the above process, let us look at some solved examples to practice the concept.

## Finding coordinates of point – Solved example

Example 01
Given below is the point P in cartesian plane. Identify the location of point.

Solution
Draw perpendicular line from point P to x & y axis.

In the above image you will observe that;

(i) The perpendicular line on x axis intersect at point 3.

It tells that horizontal distance of point is 3 units from origin.

Hence, value of x coordinate is 3.

(ii) The perpendicular line on y axis intersect at point 2.

It tells that the vertical distance of point P is 2 units.

Hence, the value of y coordinate is 2.

(iii) Using the above data, the location of point can be written as (3, 2)

Example 02
Find the location of given points P, Q & R shown in below image.

Solution
For location, draw imaginary perpendicular lines on x & y axis and note the markings.

Point P
X coordinate ⟹ -2
Y coordinate ⟹ -3
Location of Point ⟹ (-2, -3)

Point Q
X coordinate ⟹ 4
Y coordinate ⟹ -3
Location of Point ⟹ (4, -3)

Point R
X coordinate ⟹ 4
Y coordinate ⟹ 1
Location of Point ⟹ (4, 1)

Point S
X coordinate ⟹ -2
Y coordinate ⟹ 2
Location of Point ⟹ (-2, 2)

Example 03
Find the location vertex of below quadrilateral ABCD.

Solution
Draw imaginary perpendicular line on x & y axis and note the markings.

Point A
X coordinate ⟹ -5
Y coordinate ⟹ 3
Location of Point ⟹ (-5, 3)

Point B
X coordinate ⟹ -3
Y coordinate ⟹ 5
Location of Point ⟹ (-3, 5)

Point C
X coordinate ⟹ -2
Y coordinate ⟹ 3
Location of Point ⟹ (-2, 3)

Point D
X coordinate ⟹ -4
Y coordinate ⟹ 1
Location of Point ⟹ (-4, 1)

Example 04
Find the location of all vertex of below triangle.

Solution
Draw imaginary perpendicular line on x & y axis from the point A, B & C.

Point A
X coordinate ⟹ 6
Y coordinate ⟹ 3
Location of Point ⟹ (6, 3)

Point B
X coordinate ⟹ 3
Y coordinate ⟹ -2
Location of Point ⟹ (3, -2)

Point C
X coordinate ⟹ 8
Y coordinate ⟹ -3
Location of Point ⟹ (8, -3)