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प्रश्न
If point P divides segment AB in the ratio 1 : 3 where A(– 5, 3) and B(3, – 5), then the coordinates of P are ______
पर्याय
(– 2, – 2)
(– 1, – 1)
(– 3, 1)
(1, – 3)
उत्तर
(– 3, 1)
Let A(x1, y1) = A(-5, 3) and B(x2, y2) = B(3, -5),
a : b = 1 : 3
∴ x1 = -5, y1 = 3, x2 = 3, y2 = –5, a = 1, b = 3.
∴ By section formula,
|
∴ x = `(ax_2 + bx_1)/(a + b)` ∴ x = `(1(3) + 3(-5))/(1 + 3)` ∴ x = `(3 - 15)/(4)` ∴ x = `(- 12)/(4)` ∴ x = -3 |
∴ y = `(ay_2 + by_1)/(a + b)` ∴ y = `(1(-5) + 3(3))/(1 + 3)` ∴ y = `(-5 + 9)/(4)` ∴ y = `(4)/(4)` ∴ y = 1 |
∴ Co-ordinates of P are (-3, 1).
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