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