Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2:3.

If a point P(x,y) divides the line segment joining the points (-1, 7) and (4, -3) in the ratio m1 and m2, then
x = (m1x2 + m2x1) / (m1 + m2)
And y = (m1y2 + m2y1) / (m1 + m2)
Here m1 = 2, m2 = 3, x1 = -1, x2 = 4
=> x = (2 × 4 + 3 × (-1)) / (2 + 3)
=> x = (8 - 3) / 5 = 5 / 5 = 1
And y = (m1y2 + m2y1) / (m1 + m2)
Here y1 = 7, y2 = -3
=> y = (2 × (-3) + 3 × 7) / (2 + 3)
=> y = (-6 + 21) / 5 = 15 / 5 = 3
Therefore, P = (1, 3)