Question

Amara wants to draw isosceles right triangles on a coordinate plane that have two vertices at (-2, 4) and (5,4). If the coordinates of the thord vertex are both integers, how many different isosceles right triangles can she draw?

Answer 1

4

Explanation:

The given side is on the horizontal line y=4, and is of length 5-(-2) = 7. If the right angle is located at either end of this segment, the remaining vertex can be 7 units above or below that end.

The third vertex of the triangle can be located at any of the four points ...

(-2, 11), (-2, -3), (5, 11), (5, -3)

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Because the given side length is odd, using it for the hypotenuse of an isosceles right triangle would not result in integer coordinates for the right-angle vertex.