Question

On a coordinate plane, 2 lines are shown. Line C D has points (negative 2, 4) and (0, negative 4). Line F G has points (negative 4, 0) and (4, 2).

Which statement best explains the relationship between lines CD and FG?

They are perpendicular because their slopes are equal.
They are perpendicular because their slopes are negative reciprocals.
They are not perpendicular because their slopes are equal.
They are not perpendicular because their slopes are negative reciprocals

Answer 1

To determine whether the lines CD and FG are perpendicular, we need to examine the slopes of the two lines. The slope of a line is defined as the change in y divided by the change in x between any two points on the line.

For the line CD, we can use the coordinates of the two given points to calculate the slope as follows:

slope of CD = (y2 - y1) / (x2 - x1)

slope of CD = (-4 - 4) / (0 - (-2))

slope of CD = -8 / 2

slope of CD = -4

For the line FG, we can use the coordinates of the two given points to calculate the slope as follows:

slope of FG = (y2 - y1) / (x2 - x1)

slope of FG = (2 - 0) / (4 - (-4))

slope of FG = 2 / 8

slope of FG = 1/4

Now we can determine whether the slopes are negative reciprocals. Two slopes are negative reciprocals if their product is -1. Let's check:

slope of CD x slope of FG = (-4) x (1/4) = -1

Since the product of the slopes is -1, we can conclude that the lines CD and FG are perpendicular. Therefore, the statement "They are perpendicular because their slopes are negative reciprocals" is the correct statement that explains the relationship between the two lines.