Question

one line passes through the points (2,1) and (5,7). another line passes through points (-3,8) and (8,3).
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 $(2,1)$ and $(5,7)$, $m_1 = \frac{7 - 1}{5 - 2} = \frac{6}{3} = 2$.

Step2: Calculate slope of second line

For points $(-3,8)$ and $(8,3)$, $m_2 = \frac{3 - 8}{8 - (-3)} = \frac{-5}{11}$.

Step3: Check parallel or perpendicular

Parallel lines have equal slopes ($m_1 = m_2$), perpendicular lines have slopes that multiply to -1 ($m_1 \times m_2 = -1$). Here, $2
eq \frac{-5}{11}$ and $2 \times \frac{-5}{11} = \frac{-10}{11}
eq -1$.

Answer:

C. Neither