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Find the ratio in which the point (-3, k) divides the join of

Question

Find the ratio in which the point $(- 3, k)$ divides the join of $A (- 5, - 4)$ and $B (- 2, 3)$ . Also, find the value of k.

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Charlotte Discussed

Find the ratio in which the point

(- 3, k)

divides the join of

A (- 5, - 4)

and

B (- 2, 3)

. Also, find the value of k.

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

m : n

, then

- 3 = \frac{m ( - 2 ) + n ( - 5 )}{m + n}

- 3 m - 3 n = - 2 m - 5 n

- 5 n + 3 n = - 3 m + 2 m

- 2 n = - m \Rightarrow \frac{m}{n} = \frac{- 2}{- 1} = \frac{2}{1}

ratio

= m : n = 2 : 1

Now,

k = \frac{m \times 3 + n \times ( - 4 )}{m + n}

= \frac{2 \times 3 + 1 \times ( - 4 )}{2 + 1}

= \frac{6 - 4}{3} = \frac{2}{3}

The value of k is

2/3

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Question Text	Find the ratio in which the point $(- 3, k)$ divides the join of $A (- 5, - 4)$ and $B (- 2, 3)$ . Also, find the value of k.
Answer Type	Text solution:1
Upvotes	154