Question

Two vertices of a right triangle have coordinates (6, −2) and (1, 6) .

Select each ordered pair that could be the coordinates of the third vertex.

​ (6, 6) ​

​​ ​ (1, −2) ​

​ ​ (1, 1) ​ ​

​ (−2, 1) ​

Answer 1

(1, -2) (just typing this because this needs to be 20 characters long)

Answer 2

ANSWER

The coordinates of the third vertices are $(6,6)$ or $(1,-2)$.

EXPLANATION

Let the hypotenuse of the right angle triangle have vertices $(6,-2)$ and $(1,6)$.

The third point is the intersection of the horizontal line that passes through (6,-2), that has equation $y=-2$ and the vertical line that passes through $(1,6)$ which also has equation $x=1$.

Hence one possible coordinates of the third vertex is $(1,-2)$.

The third vertex could also be the intersection of the vertical line that passes through (6,-2), that has equation $x=6$ and the horizontal line that passes through $(1,6)$ which also has equation $y=6$.

Hence another possible coordinates of the third vertex is $(6,6)$.

See diagram in attachment