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Question
If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______
Options
(3, 3)
(6, 6)
(2, 2)
(1, 1)
Solution
(6, 6)
Let A(x1, y1) and B(x2, y2) = B(-1, -1)
P(x, y) = P(1, 1) divides AB in ratio 5 : 2.
∴ x1 = 1, y1 = 1, x2 = –1, y2 = –1, a = 5, b = 2.
∴ By section formula,
∴ x = `(ax_2 + bx_1)/(a + b)`
∴ `1 = (5(-1) + 2x_1)/(5 + 2)`
∴ 7 = -5 + 2x1
∴ 2x1 = 7 + 5
∴ 2x1 = 12
∴ x1 = `12/2`
∴ x1 = 6
∴ Co-ordinates of A are (6, 6).
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