# Find the Coordinates of a Point

How to find the coordinates of a point on the coordinate graph paper?

In the adjoining figure, for locating the coordinates of a point draw XOX' and YOY' are co-ordinate axes.

To locate the position of point P, we draw a perpendicular from P on X'OX, i.e., PT ┴ XOX'

So, the co-ordinate of point P are (OT, PT).

Example to find the coordinates of a point:

1. In the adjoining figure, XOX' and YOY' are the co-ordinate axes. Find out the coordinates of point A, B, C and D.

Solution:

To locate the position of point A, draw AQ ┴ X'OX.

Then the co-ordinate of point A are (OQ, QA) i.e., A (5, 2). These points lie in the I quadrant.

To locate the position of point B, draw BP ┴ X'OX.

Then the co-ordinate of point B are (OP, PB) i.e., B (-3, 4). These points lie in the II quadrant.

To locate the position of point C, draw CS ┴ X'OX.

Then the co-ordinate of point C are (OS, SC), i.e., C (-4, -2). These points lie in the III quadrant.

To locate the position of point D, draw DR ┴ X'OX.

Then the co-ordinate of point D are (OR, RD) i.e., D (3, -2). These points lie in the IV quadrant.

2. In the adjoining figure, XOX' and YOY' are the co-ordinate axes. Find out the coordinates of point P, Q, R, S, T and U. Also write the abscissa and ordinate in each case.

Solution:

To locate the position of point Q:

Point Q is the I quadrant where abscissa and ordinate both are positive.

Perpendicular distance of Q from y-axis is 4 units.

So, x-co-ordinate of Q is 4.

Perpendicular distance of Q from x-axis is 3 units.

So, y-co-ordinate of Q is 3.

Therefore, co-ordinate of Q are (4, 3).

To locate the position of point P:

Point P is the II quadrant where abscissa is negative and ordinate is positive.

Perpendicular distance of P from y-axis is 2 units.

So, x-co-ordinate of P is -2

Perpendicular distance of P from x-axis is 5 units.

So, y-co-ordinate of P is 5

Therefore, co-ordinate of P are (-2, 5)

To locate the position of point S:

Point S is the III quadrant where abscissa and ordinate both are negative.

Perpendicular distance of S from y-axis is 4 units.

So, x-co-ordinate of S is -4.

Perpendicular distance of S from x-axis is 1 unit.

So, y-co-ordinate of S is -1.

Therefore, co-ordinate of S are (-4, -1)

To locate the position of point R:

Point R is the IV quadrant where abscissa is positive and ordinate is negative.

Perpendicular distance of R from y-axis is 2 units.

So, x-co-ordinate of R is 2

Perpendicular distance of R from x-axis is 4 units.

So, y-co-ordinate of R is -4

Therefore, co-ordinate of R are (2, -4)

To locate the position of point T:

Point T is in the positive x-axis. We know, that the co-ordinate of a point on x-axis are of the form (x, 0)

Perpendicular distance of T from y-axis is 2 units.

So, x-co-ordinate of T is 2

Perpendicular distance of T from x-axis is 0 unit.

So, y-co-ordinate of T is 0

Therefore, co-ordinate of T are (2, 0)

To locate the position of point U:

Point U is in the negative y-axis. We know, that the co-ordinate of a point on y-axis are of the form (0, y)

Perpendicular distance of U from y-axis is 0 units.

So, x-co-ordinate of U is 0

Perpendicular distance of U from x-axis is 4 units.

So, y-co-ordinate of U is -4

Therefore, co-ordinate of U are (0, -4)

The above worked-out problems will help us to find the coordinates of a point on the graph paper.

Related Concepts:

Coordinate Graph

Signs of Coordinates

Find the Coordinates of a Point

Coordinates of a Point in a Plane

Plot Points on Co-ordinate Graph

Graph of Linear Equation

Simultaneous Equations Graphically

Graphs of Simple Function

Graph of Perimeter vs. Length of the Side of a Square

Graph of Area vs. Side of a Square

Graph of Simple Interest vs. Number of Years

Graph of Distance vs. Time

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Estimating Sum and Difference | Reasonable Estimate | Procedure | Math

May 22, 24 06:21 PM

The procedure of estimating sum and difference are in the following examples. Example 1: Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

2. ### Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

May 22, 24 06:14 PM

While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the digit in the hundreds place is = to or > 5…

3. ### Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

May 22, 24 05:17 PM

While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

4. ### Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

May 22, 24 03:49 PM

Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…