Question

the line shown has a slope of \\( \frac { 3 } { 2 } \\) between point l and point n and between point q and point s. which of the following is true? a. \\( \frac { m n } { l m } = \frac { q r } { q s } \\) b. \\( \frac { l m } { l n } = \frac { q s } { q r } \\) c. \\( \frac { l m } { m n } = \frac { q r } { q s } \\) d. \\( \frac { m n } { l m } = \frac { q s } { q r } \\)

Explanation:

Step1: Recall the slope formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For two right - angled triangles formed by the line (like \(\triangle LMN\) and \(\triangle QRS\)), if the slope \(m=\frac{3}{2}\), then for \(\triangle LMN\), \(m=\frac{MN}{LM}=\frac{3}{2}\), and for \(\triangle QRS\), \(m = \frac{RS}{QR}=\frac{3}{2}\).

Step2: Check the ratios

Since \(\frac{MN}{LM}=\frac{3}{2}\) and \(\frac{RS}{QR}=\frac{3}{2}\), we can say that \(\frac{MN}{LM}=\frac{RS}{QR}\)

Answer:

A. \(\frac{MN}{LM}=\frac{QR}{QS}\)