# When the coordinates (1, 1), (2, 3), (5, 3), and (4, 1) are joined, which shape is formed?

**Solution:**

First we have to calculate the distance between two points

Distance between (1, 1) and (2, 3) = √{(2 - 1)^{2} + (3 - 1)^{2}} = √5 units

Distance between (2, 3) and (5, 3) = √{(5 - 2)^{2} + (3 - 3)^{2}} = 3 units

Distance between (5, 3) and (4, 1) = √{(4 - 5)^{2} + (1 - 3)^{2}} = √5 units

Distance between (4, 1) and (1, 1) = √{(4 - 1)^{2} + (1 - 1)^{2}} = 3 units

We can observe here that two pairs of line segments are equal.

The slopes of all the curves can be found using the slope formula

Slope of line joining (1, 1) and (2, 3) = (3 - 1) / (2 - 1) = 2

Slope of line joining (2, 3) and (5, 3) = (3 - 3) / (5 - 2) = 0

Slope of line joining (5, 3) and (4, 1) = (3 - 1) / (5 - 4) = 2

Slope of line joining (1, 1) and (4, 1) = (1 - 1) / (4 - 1) = 0

We can observe that two pairs of slopes are equal.

In the shape which is formed, two pairs of lines are parallel.

Therefore, the shape formed is a parallelogram.

## When the coordinates (1, 1), (2, 3), (5, 3), and (4, 1) are joined, which shape is formed?

**Summary:**

When the coordinates (1, 1), (2, 3), (5, 3), and (4, 1) are joined, the shape formed is a parallelogram.

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