Question

The ratio in which the point (8, 7) divides the line segment joining the points $(\frac{28}{3},\frac{22}{3})and(\frac{20}{3},\frac{20}{3})$ is k:1. The value of k is _

Answer 1

Let the point C (8, 7) divide the line segment joining the points
$(\frac{28}{3},\frac{22}{3})and(\frac{20}{3},\frac{20}{3})$ in the ratio of k : 1. Then,
$C=\frac{(k\times \frac{20}{3}+\frac{28}{3})}{(k+1)}=8\Rightarrow k\times \frac{20}{3}+\frac{28}{3}=8k+8\Rightarrow k=1$
Hence the point (8, 7) divides the line segment in the ratio 1:1.