Question

Find the ratio in which the point (-6, k) divides the line segment joining the points (-3, -1) and (-8, 9). Hence find the value of k.

Answer 1

Given ,

the point (-6, k) divides the line segment joining the points (-3, -1) and (-8, 9)

Let , the point (-6, k) divides the line segment in ratio m : n

We know that , the section formula is given by

$\boxed{ \sf{x = \frac{m x_{2} + n x_{1}}{m + n} \: \: , \: \: y= \frac{m y_{2} + n y_{1}}{m + n} }}$

Thus ,

$: \mapsto \tt - 6 = \frac{m( - 8) + n( - 3)}{m + n}$

$: \mapsto \tt - 6m - 6n = - 8m - 3n$

$: \mapsto \tt 2m = 3n$

$: \mapsto \tt \frac{m}{n} = \frac{3}{2}$

The ratio in which the point (-6, k) divides the line segment joining the points (-3, -1) and (-8, 9) is 3 : 2

Now ,

$: \mapsto \tt k = \frac{3(9) + 2( - 1)}{3 +2 }$

$: \mapsto \tt k = \frac{27 - 2}{5}$

$: \mapsto \tt k = \frac{25}{5}$

$: \mapsto \tt k = 5$

The value of k is 5