We can solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

We can use coordinates to find the area of a figure and and absolute value to find distances between points with the same first coordinate or the same second coordinate.

**Example 1 :**

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

**Solution :**

From the graph, the ordered pair of A is (3, 3) and B is (3, -4)

Since, the distance is parallel to "y" axis, let us take the "y" coordinates in the two points A and B.

They are 3 and -4.

To find the distance between the two points , we have to add the absolute values of the y-coordinates

Then, the distance between the two points A and B is

= |3| + |-4|

= 3 + 4

= 7

So, the distance between points A and B is 7 units.

**Example 2 :**

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

**Solution :**

From the graph, the ordered pair of A is (3, 3) and B is (-4, 3)

Since, the distance is parallel to "x" axis, let us take the "x" coordinates in the two points A and B.

They are 3 and -4.

To find the distance between the two points , we have to add the absolute values of the x-coordinates

Then, the distance between the two points A and B is

= |3| + |-4|

= 3 + 4

= 7

So, the distance between points A and B is 7 units.

**Example 2 :**

What type of polygon can you make by plotting these points ?

Point A (-4, 2)

Point B (2, 2)

Point C (-4, -2)

Point D (2, -2)

And also find the area of the polygon made by these points.

**Solution : **

To know the type of the polygon, let us plot the given points on the coordinate plane.

When we plot the given points on the coordinate plane, it is clear that **the polygon we get is rectangle**.

Here, AB represents the length and AC represents the width of the rectangle ABCD.

To find the area of the rectangle, we have to find the length AB and width AC.

**Finding the length AB : **

From the graph, the ordered pair of A is (-4, 2) and B is (2, 2)

Since, the distance is parallel to "x" axis, let us take the "x" coordinates in the two points A and B.

They are -4 and 2.

To find the distance between the two points , we have to add the absolute values of the x-coordinates

Then, the distance between the two points A and B is

= |-4| + |2|

= 4 + 2

= 6

Therefore, the length AB is 6 units.

**Finding the width AC :**

From the graph, the ordered pair of A is (-4, 2) and B is (-4, -2)

Since, the distance is parallel to "y" axis, let us take the "y" coordinates in the two points A and B.

They are 2 and -2.

To find the distance between the two points , we have to add the absolute values of the y-coordinates

Then, the distance between the two points A and B is

= |2| + |-2|

= 2 + 2

= 4

Therefore, the width AB is 4 units.

**Finding area of the rectangle ABCD : **

Area of the rectangle ABCD is

= length x width

= 6 x 4

= 24

So, the area of the rectangle ABCD is 24 square units.

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