Question

Explain why the hypotenuses of the triangles below have the same slope.

Answer 1

The hypotenuse of the two triangles have the same slope because they are in the same straight line and the slope of a straight line is constatn.

You can prove that in this way:

slope = rise / run = Δy / Δx

For the upper triangle: slope = (4 - 2) / (8 - 4) = 2 / 4 = 1 / 2

For the lower triangle: slope = (-1 - (-5)) / (- 2 - (-10)) = 4 / 8 = 1 / 2

So, this proves that the two slopes are the same: 1 / 2