# FINDING DISTANCE IN THE COORDINATE PLANE

## About "Finding distance in the coordinate plane"

Finding distance in the coordinate plane :

We can use absolute values to find distances between two points that have the same x-coordinates or the same y-coordinates on a coordinate plane.

## Finding distance in the coordinate plane - Examples

Example 1 :

What is the distance between point A(4, 3) and point B(4, -2) ?

Solution :

Step 1 :

Find the distance between point A and the x-axis.

The y-coordinate of A is 3, so point A is |3| = 3 units from the x-axis.

Step 2 :

Find the distance between point B and the x-axis.

The y-coordinate of B is −2, so point B is |−2| = 2 units from the x-axis.

Step 3 :

Find the sum of the distances.

Distance from A to B is

= |3| + |−2| = 3 + 2 = 5 units.

The steps explained above have been illustrated in the graph given below.

Example 2 :

What is the distance between point C(-1, -4) and point D(-5, -4) ?

Solution :

Step 1 :

Find the distance between point C and the y-axis.

The x-coordinate of C is -1, so point C is |-1| = 1 unit from the y-axis.

Step 2 :

Find the distance between point D and the y-axis.

The x-coordinate of D is −5, so point B is |−5| = 5 units from the y-axis.

Step 3 :

Find the distance between C and D by finding this difference :

Distance of D from the y-axis − distance of C from the y-axis

|-5| - |-1| = 5 - 1 = 4 units.

The steps explained above have been illustrated in the graph given below.

Example 3 :

Find the distance between the points A and B in the given graph given below.

Solution :

From the graph, the ordered pair of A is (-3, -2) and B is (3, -2) respectively.

Step 1 :

Find the distance between point A and the y-axis.

The x-coordinate of A is -3, so point A is |-3| = 3 units from the y-axis.

Step 2 :

Find the distance between point B and the y-axis.

The x-coordinate of B is 3, so point B is |3| = 3 units from the y-axis.

Step 3 :

Find the sum of the distances.

Distance from A to B is

= |-3| + |3| = 3 + 3 = 6 units.

The steps explained above have been illustrated in the graph given below.

After having gone through the stuff given above, we hope that the students would have understood "How to find distance in the coordinate plane".

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