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

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

The correct answer :Let the coordinates of the required point be (x, y).

Using the section formula, we have:

x = [ (3 * (-1)) + (2 * 4) ] / (2 + 3) = [ -3 + 8 ] / 5 = 1

y = [ (3 * 7) + (2 * (-3)) ] / (2 + 3) = [ 21 – 6 ] / 5 = 3

Therefore, the point which divides the join of A(-1, 7) and B(4, -3) in the ratio 2:3 is (1, 3).