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Question
The point Q divides segment joining A(3, 5) and B(7, 9) in the ratio 2 : 3. Find the X-coordinate of Q
Solution
Let the co-ordinates of point Q be (x, y) and A (x1, y1), B (x2, y2) be the given points.
Here, x1 = 3, y1 = 5, x2 = 7, y2 = 9, m = 2, n = 3
∴ By section formula,
x = `("m"x_2 + "n"x_1)/("m" + "n")`
= `(2(7) + 3(3))/(2 + 3)`
= `(14 + 9)/5`
= `23/5`
y = `("m"y_2 + "n"y_1)/("m" + "n")`
= `(2(9) + 3(5))/(2 + 3)`
= `(18 + 15)/5`
= `33/5`
∴ The co-ordinates of point Q are `(23/5, 33/5)`.
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