Question

1. given points a(?, 5), b(-2, -1), c(1, 1), and d(3, 5), what type of lines are $overline{ab}$ and $overline{bc}$?

$m = \frac{y_1 - y_2}{x_1 - x_2}=$______

Explanation:

Step1: Calculate slope of line $\overline{AB}$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $A(x_1,y_1)$ and $B(x_2,y_2)$ where $A(1,5)$ and $B(- 2,-1)$, we have $m_{AB}=\frac{-1 - 5}{-2 - 1}=\frac{-6}{-3}=2$.

Step2: Calculate slope of line $\overline{BC}$

For points $B(x_1,y_1)=(-2,-1)$ and $C(x_2,y_2)=(1,1)$, we use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m_{BC}=\frac{1-(-1)}{1-(-2)}=\frac{1 + 1}{1 + 2}=\frac{2}{3}$.

Step3: Analyze the relationship between the lines

Since the slopes $m_{AB}=2$ and $m_{BC}=\frac{2}{3}$ are both non - zero and not equal, the lines $\overline{AB}$ and $\overline{BC}$ are neither parallel nor perpendicular.

Answer:

The lines $\overline{AB}$ and $\overline{BC}$ are two non - parallel and non - perpendicular lines.