Question

write whether the lines that contain these pairs of points are parallel, perpendicular, or neither. 10. (6, -2) and (8, -3); (15, 9) and (13, 8) 11. (4, -9) and (5, 5); (6, 5) and (-8, 6)

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope for first pair in 10.

For points $(6,-2)$ and $(8,-3)$, $m_1=\frac{-3-(-2)}{8 - 6}=\frac{-3 + 2}{2}=-\frac{1}{2}$. For points $(15,9)$ and $(13,8)$, $m_2=\frac{8 - 9}{13 - 15}=\frac{-1}{-2}=\frac{1}{2}$. Since $m_1
eq m_2$ and $m_1\times m_2=-\frac{1}{2}\times\frac{1}{2}=-\frac{1}{4}
eq - 1$, the lines are neither parallel nor perpendicular.

Step3: Calculate slope for first pair in 11.

For points $(4,-9)$ and $(5,5)$, $m_3=\frac{5-(-9)}{5 - 4}=\frac{5 + 9}{1}=14$. For points $(6,5)$ and $(-8,6)$, $m_4=\frac{6 - 5}{-8 - 6}=\frac{1}{-14}=-\frac{1}{14}$. Since $m_3\times m_4=14\times(-\frac{1}{14})=-1$, the lines are perpendicular.

Answer:

1. Neither
2. Perpendicular