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

Lines A and B are perpendicular.

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}=(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=(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}=(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=(-2-\left(-3\right))/(2-0)`

`m=(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.