Question

In the adjacent figure $XY\parallel BC$ find the length of $AY$ and $CY$

Answer 1

$XY\parallel BC$

$\Rightarrow \angle AXY=\angle ABC$ and $\angle AYX=\angle ACB$(corresponding angles)

$\Rightarrow △AXY\sim △ABC$ by AA similarity

$\Rightarrow \frac{AX}{AB}=\frac{AY}{AC}=\frac{XY}{BC}$

$\Rightarrow \frac{1}{AX+XB}=\frac{AC-YC}{AC}$

$\Rightarrow \frac{1}{4}=\frac{6-YC}{6}$

$\Rightarrow 24-4YC=6$

$\Rightarrow -4YC=6-24=-18$

$\therefore YC=\frac{-18}{-4}=4.5$cm

$AY=AC-YC=6-4.5=1.5$cm

$\therefore AY=1.5$cm and $CY=4.5$cm