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  • Find the ratio in which x-3y=0 divides the line segment joining the points A( -2,-5) and B (6,3) and also find the coordinates of the point .

Find the ratio in which x-3y=0 divides the line segment joining the points A( -2,-5) and B (6,3) and also find the coordinates of the point .

Answers (1)

best_answer

Given line: x - 3y = 0
Points: A(-2, -5), B(6, 3)

Let the point divide AB in the ratio m:n.

Using section formula, coordinates of the point are:
((6m - 2n)/(m+n), (3m - 5n)/(m+n))

Since the point lies on x - 3y = 0, substitute:

(6m - 2n) - 3(3m - 5n) = 0

6m - 2n - 9m + 15n = 0

-3m + 13n = 0

Therefore,
m:n = 13:3

Now finding coordinates:

x = (6×13 - 2×3)/16 = 72/16 = 9/2

y = (3×13 - 5×3)/16 = 24/16 = 3/2

Final Answer:
Ratio = 13:3
Coordinates of the point = (9/2, 3/2)

Posted by

ANKITA YADAV

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