Find the slopes of both lines.
The slope of a line can be found through the following formula:
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Find two points on both lines.
For line HJ, the line goes through (-2, 1) and (0,4). Plug these values into the formula:
[tex]\frac{4 - 1}{0-(-2)} = \frac{3}{2}[/tex]
The slope of line HJ is 3/2.
For line FG, the line goes through (-4, 1) and (0,-2). Plug these values into the formula:
[tex]\frac{-2 - 1}{0 - (-4)} = \frac{-3}{4}[/tex]
The slope of line FG is -3/4.
Compare the slopes to each other:
3/2, -3/4
They are not negative reciprocals, as the negative reciprocal of 3/2 would be -2/3, and the negative reciprocal of -3/4 would be 4/3.
The answer is d) They are not perpendicular because their slopes are not negative reciprocals.
