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

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

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)`