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

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

Step-by-step 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