Question

Suppose two adjacent endpoint of a rotated square are located at (-4, -6) and (5, -1) on the coordinates axes. What is the length of the side of the square?

Answer 1

To find the length of the side of the square, we just need to find the distance between the two endpoints. This problem can quickly be solved by using the distance formula, but for those who are not familiar with it, we can simply solve it by analyzing a triangle.

Take a look at the diagram below. We are interested in x. To find this we have created a right triangle. The horizontal component is just the distance between the x coordinates of the two points while the vertical component is the distance between the y coordinates.

The horizontal component is 9 and the vertical component is 5. We can now get x by using the pythagorean theorem:

$x^{2}= 9^{2} + 5^{2} =81+25=106$
$x= \sqrt{106}$ which is approximately equal to 10.30 units.

ANSWER: The length of the side of the square measures 10.30 units.