Question

28 find the slope of $overleftrightarrow{ma}$ and $overleftrightarrow{th}$. then determine if the lines are parallel, perpendicular or neither.
$m(1,9), a(7,4), t(8,13), h(-2,1)$
$moverleftrightarrow{ma} = square$
$moverleftrightarrow{th} = square$
lines are $square$

Explanation:

Step1: Calculate slope of $\overleftrightarrow{MA}$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ for $M(1,9), A(7,4)$:
$m_{\overleftrightarrow{MA}}=\frac{4-9}{7-1}=\frac{-5}{6}$

Step2: Calculate slope of $\overleftrightarrow{TH}$

Use slope formula for $T(8,13), H(-2,1)$:
$m_{\overleftrightarrow{TH}}=\frac{1-13}{-2-8}=\frac{-12}{-10}=\frac{6}{5}$

Step3: Check parallel/perpendicular

Parallel slopes equal; perpendicular slopes multiply to $-1$.
$\frac{-5}{6} \times \frac{6}{5} = -1$

Answer:

$m_{\overleftrightarrow{MA}} = \boldsymbol{-\frac{5}{6}}$
$m_{\overleftrightarrow{TH}} = \boldsymbol{\frac{6}{5}}$
Lines are $\boldsymbol{perpendicular}$