Point P divides the line segment joining A(−2, 3) and B(6, −5) internally in the ratio AP : PB = 3 : 1. What are the coordinates of P?

Question

Accepted Answer

(4, −3). By the section formula, P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n)) with m : n = 3 : 1. So P = ((3·6 + 1·(−2))/4, (3·(−5) + 1·3)/4) = (16/4, −12/4) = (4, −3).

Point P divides the line segment joining A(−2, 3) and B(6, −5) internally in the ratio AP : PB = 3 : 1. What are the coordinates of P?

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