What is the distances for (5,3) and (-1,-5) ?

1 Answer
Apr 22, 2018

The distance between those points is 10

Explanation:

The distance between these two points can be drawn as the hypotenuse of a right triangle.

The legs of this triangle are the lengths of the vertical and horizontal lines that you can draw to meet each other.

The distance along the x axis is the distance between the two x points 5 and -1
5 - (-1) = the horizontal distance between the points
That is a distance of 6 points.

The vertical distance up the y axis is the difference between the two y values, namely 3 - (-5), which is a distance of 8.

These are the legs of the right triangle you can draw to find the length of the hypotenuse.

The Pythagorean Theorem states that
a^2 + b^2 = c^2
6^2 + 8^2 = c^2

Since these sides form a 3-4-5 right triangle, then the length of the hypotenuse must be 10.