Question

Find the ratio in which the line segment joining the points $(-3,10)$ and $(6,-8)$ is divided by x-axis and y-axis respectively. Also find the coordinates of points of division.

Answer 1

$C$:-prove that intersection with $x-axis$.

$D$:- prove that intersection with $y-axis$.

$\begin{array}{c}y+8=\frac{18}{-9}\left(x-6\right)\\ y+8=-2x+12\\ 2x+y=4\\ \frac{AC}{CB}=\frac{\sqrt{25+100}}{\sqrt{16+14}}=\frac{\sqrt{125}}{\sqrt{80}}\\ =\frac{5\sqrt{5}}{2\sqrt{20}}\\ \frac{AC}{CB}=\frac{5\sqrt{5}}{2\sqrt{20}}\\ AC:CB=5:4\\ \frac{AD}{DB}=\frac{\sqrt{45}}{\sqrt{36+144}}=\frac{\sqrt{45}}{\sqrt{180}}=\frac{1}{2}\\ AD:DB=1:2\end{array}$

Hence,

We get $1:2$