Find the ratio in which the point divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.

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Solution

Q.
Find the ratio in which the point $(\frac{8}{5}, y)$ divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.

Ans.
$(\frac{13}{5})$

Let the ratio be k : 1 then by using section formula we have

$\frac{8}{5} = \frac{2 k + 1}{k + 1} \Rightarrow 8 k + 1 = 10 k + 5 \Rightarrow 2 k = 3 \Rightarrow k = \frac{3}{2}$

Hence the required ratio is 3 : 2.

Now, $y = \frac{3 k + 2}{k + 1} = \frac{3 \frac{3}{2} + 2}{\frac{3}{2} + 1} = \frac{9 + 4}{5} = \frac{13}{5}$

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