Question

one line passes through the points $(-3, -1)$ and $(1, -9)$. another line passes through points $(1, 4)$ and $(5, 6)$. are the lines parallel, perpendicular, or neither? choose 1 answer: a parallel b perpendicular c neither

Explanation:

Step1: Calculate slope of first line

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-3, -1)$ and $(1, -9)$, $x_1=-3, y_1=-1, x_2=1, y_2=-9$. So $m_1 = \frac{-9 - (-1)}{1 - (-3)} = \frac{-8}{4} = -2$.

Step2: Calculate slope of second line

For points $(1, 4)$ and $(5, 6)$, $x_1=1, y_1=4, x_2=5, y_2=6$. Using slope formula, $m_2 = \frac{6 - 4}{5 - 1} = \frac{2}{4} = \frac{1}{2}$.

Step3: Check relationship between slopes

Two lines are perpendicular if the product of their slopes is $-1$. Here, $m_1 \times m_2 = -2 \times \frac{1}{2} = -1$. So the lines are perpendicular.

Answer:

B. Perpendicular