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)