Find the coordinates of a point R which divides the line segment joining the points P(-2,3) and Q(4,7) internally in the ratio 4:7.

Let the coordinate of R be (x, y)

P (-2, 3 ) where x₁ = -2 and y₁ = 3

R (4, 7) where x₂ = 4 and y₂ = 7

m: n ratio given is 4: 7.

Therefore, coordinate of R is:

x = [(4 × 4) + (7 × -2) ]/ (4 + 7)  and y  = [(4 × 7) + (7 × 3) ]/ (4 + 7)

x = 2/ 11 and y = 49/11.

Hence coordinate of R : (2/11, 49/11)