Question

Determine the relationship between Line AB (points: (6, -6) and (-8, 3)) and Line CD (points: (-9, -1) and (0, -15))—parallel, perpendicular, or neither.

Answer 1

Line AB with a slope of -9/14 and Line CD with a slope of -14/9 are perpendicular to each other as their slopes are negative reciprocals.

Step-by-step explanation:

The relationship between Line AB and Line CD can be determined by finding the slopes of each line and comparing them.

To find the slope of Line AB, with points (6, -6) and (-8, 3), use the formula (y2 - y1) / (x2 - x1), which gives us (3 - (-6)) / (-8 - 6) = 9 / -14.

The slope of Line AB is -9/14. Next, find the slope of Line CD, with points (-9, -1) and (0, -15), using the same formula, which gives us (-15 - (-1)) / (0 - (-9)) = -14 / 9. The slope of Line CD is -14/9.

Since the slopes of the two lines are negative reciprocals of each other, it indicates that the lines are perpendicular to each other.

Lines that are perpendicular form a 90-degree angle with each other.