Question:

Find the ratio in which point T(-1, 6)divides the line segment joining the points P(-3, 10) and Q(6, -8).

Answer:

Let, point T(-1,6) divides segment PQ in the ratio m:n
Given P(-3, 10) and Q(6, -8).
x = -1 , y = 6
x₁= -3 , y₁= 10
x₂= 6 , y₂= -8
By Section formula, x = (mx₂+nx₁)/(m+n)
-1 = m×6+n×-3/(m+n)
-1 = 6m-3n/(m+n)
-m+-n = 6m-3n
2n = 7m
m/n = 2/7
m:n = 2:7
Point T divides PQ is the ratio 2:7.

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Find the ratio in which point T(-1, 6)divides the line segment joining the points P(-3, 10) and Q(6, -8).

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