ANSWER
The coordinates of point R in the first quadrant are [tex]R(1,6)[/tex].
EXPLANATION
We were given that the hypotenuse of the right angle triangle has vertices [tex]P(-3,6)[/tex] and [tex]Q(1,4)[/tex].
The third point R is the intersection of the horizontal line that passes through [tex]P(-3,6)[/tex], that has equation [tex]y=6[/tex] and the vertical line that passes through[tex]Q(1,4)[/tex] which also has equation [tex]x=1[/tex].
Hence one possible coordinates of point R is [tex](1,6)[/tex] which lies in the first quadrant.
The third point T could also be the intersection of the vertical line that passes through [tex]P(-3,6)[/tex], that has equation [tex]x=-3[/tex] and the horizontal line that passes through [tex]Q(1,4)[/tex] which also has equation [tex]y=4[/tex].
Hence another possible coordinates of point R is [tex](-3,4)[/tex] which lies in the third quadrant.
Therefore the required coordinates of R is [tex](1,6)[/tex]
See diagram in attachment
