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Point A lies on the line segment PQ joining P(6, -6) and Q(-4,

Question

Point A lies on the line segment PQ joining $P (6, - 6)$ and $Q (- 4, - 1)$ in such a way that $P A / PQ = 2/5$ . If the point A also lies on the line $3 x + k (y + 1) = 0$ , find the value of k.

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Point A lies on the line segment PQ joining

P (6, - 6)

and

Q (- 4, - 1)

in such a way that

P A / PQ = 2/5

. If the point A also lies on the line

3 x + k (y + 1) = 0

, find the value of k.

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Text solutionVerified

Let the point

A (x, y)

which lies on line joining

P (6, - 6)

and

Q (- 4, - 1)

such that

P A / PQ = 2/5

Line segment PQ is divided by the point A in the ratio

2 : 3

Step

1

: Find coordinates of

A (x, y)

x = \frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}

x = (2 (- 4) + 3 (6)) / (2 + 3)

= (- 8 + 18) /5

= 10/5 = 2

y = \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}}

y = (2 (- 1) + 3 (- 6)) /5

= (- 2 - 18) /5

= - 20/5

= - 4

Step

2

: Point A also lies on the line

3 x + k (y + 1) = 0

3 (2) + k (- 4 + 1) = 0

6 - 3 k = 0

k = 2

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Question Text	Point A lies on the line segment PQ joining $P (6, - 6)$ and $Q (- 4, - 1)$ in such a way that $P A / PQ = 2/5$ . If the point A also lies on the line $3 x + k (y + 1) = 0$ , find the value of k.
Answer Type	Text solution:1
Upvotes	151