Question

line g passes through points (10, 10) and (2, 17). line h passes through points (2, 2) and (10, 9). are line g and line h parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Calculate slope of line g

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For line $g$ with points $(x_1,y_1)=(10,10)$ and $(x_2,y_2)=(2,17)$, we have $m_g=\frac{17 - 10}{2 - 10}=\frac{7}{-8}=-\frac{7}{8}$.

Step2: Calculate slope of line h

For line $h$ with points $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(10,9)$, we have $m_h=\frac{9 - 2}{10 - 2}=\frac{7}{8}$.

Step3: Check parallel and perpendicular conditions

Two lines are parallel if $m_1 = m_2$. Here $m_g
eq m_h$. Two lines are perpendicular if $m_1\times m_2=- 1$. Here $m_g\times m_h=(-\frac{7}{8})\times\frac{7}{8}=-\frac{49}{64}
eq - 1$.

Answer:

neither