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Find the ratio in which the line segment joining the points (-

Question

Find the ratio in which the line segment joining the points $(- 3, 10)$ and $(6, - 8)$ is divided by $(- 1, 6)$ .

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Olivia Discussed

Find the ratio in which the line segment joining the points

(- 3, 10)

and

(6, - 8)

is divided by

(- 1, 6)

13 mins ago

Discuss this question LIVE

13 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 the required ratio be

m_{1} : m_{2}

Take

(x_{1}, y_{1}) = (- 3, 10); (x_{2}, y_{2}) = (6, - 8)

and

(x, y) = (- 1, 6)

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

\Rightarrow - 1 = \frac{m _{1} \times 6 + m _{2} \times - 3}{m _{1} + m _{2}}

\Rightarrow - m_{1} - m_{2} = 6 m - 3 m_{2}

\Rightarrow - m_{1} - 6 m_{1} = - 3 m_{2} + m_{2}

\Rightarrow - 7 m_{1} = - 2 m_{2}

\Rightarrow \frac{m _{1}}{m _{2}} = \frac{2}{7}

∴

The required ratio is

2 : 7

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Question Text	Find the ratio in which the line segment joining the points $(- 3, 10)$ and $(6, - 8)$ is divided by $(- 1, 6)$ .
Answer Type	Text solution:1
Upvotes	150