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प्रश्न
Find the ratio in which Y-axis divides the point A(3, 5) and point B(– 6, 7). Find the coordinates of the point
उत्तर
Let C be a point on Y-axis which divides seg AB in the ratio m : n
Point C lies on the Y-axis.
∴ its X-coordinate is 0.
Let C = (0, y)
Here,
A(x1, y1) = A(3, 5)
B(x2, y2) = B(– 6, 7)
By Section formula,
x = `("m"x_2 + "n"x_1)/("m" + "n")`
∴ 0 = `(-6"m" + 3"n")/("m" + "n")`
∴ – 6m + 3n = 0
∴ 3n = 6m
∴ `"m"/"n" = 3/6`
∴ `"m"/"n" = 1/2` ......(i)
∴ m : n = 1 : 2
By section formula,
y = `("m"y_2 + "n"y_1)/("m" + "n")`
y = `(7"m" + 5"n")/("m" + "n")`
= `(7"m" + 5(2"m"))/("m" + 2"m")` ......[From (i), n = 2m]
= `(7"m" + 10"m")/(3"m")`
= `(17"m")/(3"m")`
∴ Y-axis divides the seg AB in the ratio 1 : 2 and the co-ordinates of that point is `(0, 17/3)`.
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