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Find te ratio in which the line segment joining A(1, -5) and B

Question

Find te ratio in which the line segment joining $A (1, - 5)$ and $B (- 4, 5)$ is divided by the $x -$ axis. Also find the coordinates of the point of division.

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Find te ratio in which the line segment joining

A (1, - 5)

and

B (- 4, 5)

is divided by the

x -

axis. Also find the coordinates of the point of division.

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Let

A (1, - 5)

and

B (- 4, 5)

be divided by the

x -

axis in the ratio

k : 1

\Rightarrow y = 0

Using section formula, we have

(x, y) = (\frac{- 4 k + 1}{k + 1}, \frac{5 k - 5}{k + 1})

\Rightarrow (x, 0) = (\frac{- 4 k + 1}{k + 1}, \frac{5 k - 5}{k + 1})

Equating, we get

\frac{5 k - 5}{k + 1} = 0

\Rightarrow 5 k - 5 = 0

\Rightarrow 5 k = 5

k = 1

Thus, the point divides in the ratio

1 : 1

which is a mid-point.

\Rightarrow (x, y) \equiv (\frac{- 4 + 1}{2}, \frac{- 5 + 5}{2}) \equiv (- \frac{3}{2}, 0)

Hence the coordinates of the point of division is

(- \frac{3}{2}, 0)

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Question Text	Find te ratio in which the line segment joining $A (1, - 5)$ and $B (- 4, 5)$ is divided by the $x -$ axis. Also find the coordinates of the point of division.
Answer Type	Text solution:1
Upvotes	150