Question

ilarity transformations
which value of y would make \\(\overline{op} \parallel \overline{ln}\\)?
16
24
36
32

Explanation:

Step1: Apply the Basic Proportionality Theorem (Thales' theorem)

If \( \overline{OP} \parallel \overline{LN} \), then by the Basic Proportionality Theorem, \( \frac{MO}{OL} = \frac{MP}{PN} \).

We know \( MO = 28 \), \( OL = 14 \), and \( PN = 18 \). Let \( MP = y \). So the proportion is \( \frac{28}{14} = \frac{y}{18} \).

Step2: Simplify the left - hand side of the proportion

Simplify \( \frac{28}{14} \), we get \( \frac{28}{14}=2 \). So the equation becomes \( 2=\frac{y}{18} \).

Step3: Solve for \( y \)

To solve for \( y \), we multiply both sides of the equation \( 2=\frac{y}{18} \) by 18. So \( y = 2\times18=36 \).

Answer:

36