Answer:
(c)
Step-by-step explanation:
Consider ΔXBY and ΔABC
∠XYB = ∠ACB [ Corresponding angles of parallel line (AC and XY) are equal]
∠XBY = ∠ABC (Common angles)
By AA similarity, ΔXBY [tex] \sim[/tex] ΔABC,
We know that the ratio of area of two similar triangles is the square of ratios of their sides.
Ratio of sides = [tex]\frac{XY}{AC}[/tex]
= [tex]\frac{2}{3}[/tex]
[tex]\frac{Area of \triangle XBY}{Area of \triangle ABC}[/tex] = [tex][\frac{XY}{AC}]^{2}[/tex]
= [tex][\frac{3}{2}]^{2}[/tex]
= [tex]\frac{4}{9}[/tex]
Option (c) is correct
