Question

Line A goes through points (-2,3) and (-1,1). Line B goes through points (0,-3) and (2,-2).

Fill in the blank: Lines A and B are ______.

Answer 1

i believe perpendicular

Answer 2

Answer:

Lines A and B are perpendicular.

Step-by-step explanation:

Line A goes through points (-2,3) and (-1,1).

Finding the slope of line A

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:3\right),\:\left(x_2,\:y_2\right)=\left(-1,\:1\right)$

$m=\frac{1-3}{-1-\left(-2\right)}$

$m=-2$

Line B goes through points (0,-3) and (2,-2).

Finding the slope of line B

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:-3\right),\:\left(x_2,\:y_2\right)=\left(2,\:-2\right)$

$m=\frac{-2-\left(-3\right)}{2-0}$

$m=\frac{1}{2}$

Please note that the slope of line A is a negative reciprocal of line B and vice versa.

As we know that the slopes of two perpendicular lines are negative reciprocals of each other.

Therefore, lines A and B are perpendicular.