Question

State whether the lines will be parallel, perpendicular, or neither. AB: (0,2) and (5,4) CD: (1,8) and (3,3)?

a) Parallel
b) Perpendicular
c) Neither
d) Insufficient information to determine

Answer 1

By calculating the slopes of lines AB and CD, we determine that they are perpendicular as the slopes are negative reciprocals of each other.

Step-by-step explanation:

To determine if the lines will be parallel, perpendicular, or neither, we need to compare their slopes. The slope of a line can be found using the formula (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two different points on the line.

For line AB, with points (0,2) and (5,4), the slope is (4 - 2) / (5 - 0) = 2 / 5.

For line CD, with points (1,8) and (3,3), the slope is (3 - 8) / (3 - 1) = -5 / 2.

Since the slopes of AB and CD are negative reciprocals of one another, the lines are perpendicular.