According to the question,

Given,

PR = PQ

→

∴ RQ:PR = 2:3

Or

PR:RQ = 3:2

Let’s take,

R (x, y) be the point which divides the line segment joining the points P ( - 1, 3) and Q (2, 5) in the ratio 3:2

∴ (x, y) =

∵ By internal section formula;

=

Hence, the required coordinates of the point R is.