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Question
Find the ratio in which the line segment joining the points A(3, 8) and B(–9, 3) is divided by the Y– axis.
Solution
Let C be a point on Y-axis which divides seg AB in the ratio m: n.
Point C lies on the Y-axis. Thus, its x coordinate is 0.
Let C = (0, y)
∴ x1 = −9, y1 = 3, x2 = 3, y2 = 8
∴ By section formula,
`"x" = ("mx"_2 + "nx"_1)/"m + n"`
∴ `0 = "m × 3 + n × −9"/"m + n"`
∴ `0 = "3m − 9n"/"m + n"`
∴ 0 = 3m − 9n
∴ 9n = 3m
∴ `"m"/"n" = 9/3`
∴ `"m"/"n" = 3/1`
∴ m : n = 3 : 1
Y-axis divides the seg AB in the ratio 3: 1.
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