Question

line p passes through points (10, 2) and (1, 10). line q is perpendicular to p. what is the slope of line q? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Find slope of line p

Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(10, 2)$ and $(1, 10)$, $m_p = \frac{10 - 2}{1 - 10} = \frac{8}{-9} = -\frac{8}{9}$.

Step2: Find slope of line q (perpendicular)

Perpendicular slopes are negative reciprocals. So $m_q = -\frac{1}{m_p} = -\frac{1}{-\frac{8}{9}} = \frac{9}{8}$.

Answer:

$\frac{9}{8}$