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)