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Find the ratio in which the point P(m, 6) divides the join of

Question

Find the ratio in which the point $P (m, 6)$ divides the join of $A (- 4, 3)$ and $B (2, 8)$ . Also, find the value of m.

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Evelyn Discussed

Find the ratio in which the point

P (m, 6)

divides the join of

A (- 4, 3)

and

B (2, 8)

. Also, find the value of m.

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Using the section formula, if a point

(x, y)

divides the line joining the points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

in the ratio

m : n

, then

(x, y) = (\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})

Let P divides the join of A and B in the ratio

k : 1

, then

Therefore, we have

6 = (k \times 8 + 1 \times 3) / (k + 1)

\Rightarrow 6 k + 6 = 8 k + 3

k = 3/2

P divides the join of A and B in the ratio

3 : 2

Now,

m = (2 k - 4) / (k + 1) = (2 \times 3/2 - 4) / (3/2 + 1)

= - 1/ (5/2)

= - 2/5

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Question Text	Find the ratio in which the point $P (m, 6)$ divides the join of $A (- 4, 3)$ and $B (2, 8)$ . Also, find the value of m.
Answer Type	Text solution:1
Upvotes	150