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In what ratio does the point P(2, 5) divide the join of A(8, 2

Question

In what ratio does the point $P (2, 5)$ divide the join of $A (8, 2)$ and $B (- 6, 9)?$

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In what ratio does the point

P (2, 5)

divide the join of

A (8, 2)

and

B (- 6, 9)?

11 mins ago

Discuss this question LIVE

11 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})

Given:

P (2, 5)

divides the line segment joining the points

A (8, 2)

and

B (- 6, 9)

Let P divides the AB in the ratio

m : n

2 = \frac{m x _{2} + n x _{1}}{m + n} = \frac{m ( - 6 ) + n \times 8}{m + n}

2 m + 2 n = - 6 m + 8 n

2 m + 6 m = 8 n - 2 n

\Rightarrow 8 m = 6 n

\frac{m}{n} = \frac{6}{8} = \frac{3}{4}

Ratio

= 3 : 4

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Question Text	In what ratio does the point $P (2, 5)$ divide the join of $A (8, 2)$ and $B (- 6, 9)?$
Answer Type	Text solution:1
Upvotes	151