Question

Randy wants to draw isosceles right triangles on a coordinate plane that have two vertices at (-1,6) and (-1,-2). If the coordinates of the third vertex are both integers, how many different isosceles right triangles can she draw?

Answer 1

Answer:

Two isosceles right triangles. $p_{3} = (-9,-2)$ and $p_{3'} = (7,-2)$

Step-by-step explanation:

The length of one side is:

$l_{1} = \sqrt{[-1 - (-1)]^{2}+[6 - (-2)]^{2}}$

$l_{1} = 8$

An isosceles right has two sides of identical length, which are both legs and perpendicular to each other. There are two possibilities:

$p_{3} = (-1 - 8, -2)$

$p_{3} = (-9,-2)$

$p_{3'} = (-1 + 8, -2)$

$p_{3'} = (7,-2)$