Question

The points P(−3, 6) and Q(1, 4) are two vertices of right triangle PQR . The hypotenuse of the triangle is PQ¯¯¯¯¯ . Point R lies in quadrant 1. What are the the coordinates of point R?

Answer 1

It could be (1,6) or (-3,4)

Answer 2

The coordinates of point R in the first quadrant are
`R(1,6)`.

Step-by-step explanation

We were given that the hypotenuse of the right angle triangle has vertices
`P(-3,6)` and
`Q(1,4)`.

The third point R is the intersection of the horizontal line that passes through
`P(-3,6)`, that has equation
`y=6` and the vertical line that passes through
`Q(1,4)` which also has equation
`x=1`.

Hence one possible coordinates of point R is
`(1,6)` which lies in the first quadrant.

The third point T could also be the intersection of the vertical line that passes through
`P(-3,6)`, that has equation
`x=-3` and the horizontal line that passes through
`Q(1,4)` which also has equation
`y=4`.

Hence another possible coordinates of point R is
`(-3,4)` which lies in the third quadrant.

Therefore the required coordinates of R is
`(1,6)`

See diagram in attachment