Question

4
type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
triangle abc is defined by the points a(2,9), b(8,4), and c(-3,-2).
complete the following equation for a line passing through point c and perpendicular (overline{ab}).
(y = square x + square)

Explanation:

Step1: Find slope of AB

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $A(2,9)$ and $B(8,4)$, $m_{AB}=\frac{4 - 9}{8 - 2}=\frac{-5}{6}$.

Step2: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope $m$ is the negative reciprocal, so $m_{\perp}=-\frac{1}{m_{AB}}=\frac{6}{5}$.

Step3: Use point - slope form for line through C

Point - slope form is $y - y_1 = m(x - x_1)$. For point $C(-3,-2)$ and $m=\frac{6}{5}$, we have $y - (-2)=\frac{6}{5}(x - (-3))$.
Simplify: $y + 2=\frac{6}{5}(x + 3)$.
Expand: $y+2=\frac{6}{5}x+\frac{18}{5}$.
Subtract 2 (which is $\frac{10}{5}$) from both sides: $y=\frac{6}{5}x+\frac{18}{5}-\frac{10}{5}=\frac{6}{5}x+\frac{8}{5}$.

Answer:

$\frac{6}{5}$; $\frac{8}{5}$