Question

line s passes through points (10, 4) and (3, 10). line t passes through points (8, 5) and (2, 12). are line s and line t parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Calculate slope of line s

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For line s with points $(10,4)$ and $(3,10)$, we have $m_s=\frac{10 - 4}{3 - 10}=\frac{6}{-7}=-\frac{6}{7}$.

Step2: Calculate slope of line t

For line t with points $(8,5)$ and $(2,12)$, using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, we get $m_t=\frac{12 - 5}{2 - 8}=\frac{7}{-6}=-\frac{7}{6}$.

Step3: Check relationship between slopes

Parallel lines have equal slopes. Since $m_s
eq m_t$, they are not parallel. Perpendicular lines have slopes whose product is - 1. $m_s\times m_t=(-\frac{6}{7})\times(-\frac{7}{6}) = 1
eq - 1$, so they are not perpendicular.

Answer:

neither