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Question
P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.
Solution
Given, P(1, -2), A(3, -6) and B(x,y)
AP:PB = 2:3
Hence, coordinates of P = `((2xxx+3xx3)/(2+3), (2xxy+3xx(-6))/(2+3)) = ((2x + 9)/5, (2y- 18)/5)`
But, the coordinates of P are (1, 2).
∴ `(2x + 9)/5 = 1` and `(2y - 18)/5 = -2`
⇒ 2x + 9 = 5 and 2y - 18 =-10
⇒ 2x = -4 and 2y = 8
⇒ x = -2 and y = 4
Hence, the coordinates of B are (-2,4).
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