calculate:
$\frac{A Y}{Y C}$

\frac{2}{1}

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\frac{3}{2}

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\frac{4}{9}

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\frac{5}{3}

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Solution

The correct option is A $\frac{2}{1}$
In $△ A X Y$ and $△ A B C$
$∠ X A Y = ∠ B A C$ (Common angle)
$∠ A X Y = ∠ A B C$ (Corresponding angles for parallel lines XY and BC)
$∠ A Y X = ∠ A C B$ (Corresponding angles for parallel lines XY and BC)
Thus, $△ A X Y \sim △ A B C$ (AAA rule)
Hence, $\frac{A B}{A X} = \frac{A C}{A Y}$ (Corresponding sides)
$\frac{A B}{A X} - 1 = \frac{A C}{A Y} - 1$
$\frac{A B - A X}{A X} = \frac{A C - A Y}{A Y}$
$\frac{X B}{A X} = \frac{Y C}{A Y}$
$\frac{1.5}{3} = \frac{Y C}{A Y}$
or $\frac{A Y}{Y C} = 2$

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