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Find the ratio in which the point P(x, 2) divides the join of

Question

Find the ratio in which the point $P (x, 2)$ divides the join of $A (12, 5)$ and $B (4, - 3)$ .

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Find the ratio in which the point

P (x, 2)

divides the join of

A (12, 5)

and

B (4, - 3)

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})

If point

P (x, 2)

divides the join of

A (12, 5)

and

B (4, - 3)

, then

Using section formula, we get

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

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

\Rightarrow 5 m = 3 n

\Rightarrow \frac{m}{n} = m : n = 3 : 5

The required ratio is

3 : 5

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Question Text	Find the ratio in which the point $P (x, 2)$ divides the join of $A (12, 5)$ and $B (4, - 3)$ .
Answer Type	Text solution:1
Upvotes	150