Consider the coordinates given and decide whether BC and DE are parallel, perpendicular, or neither
B(3, -3), C(-3, -7), D(6, -5), E(0, 4)
B(4, -7), C(1, 2), D(2, -8), E(-4, 10)
B(-4, 0), C(2, 2), D(1, 4), E(2, 7)
To determine whether two lines are parallel, perpendicular, or neither, we need to calculate the slopes of the lines.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).
Let's calculate the slopes for the given line segments:
For line BC:
- Coordinates B(3, -3) and C(-3, -7)
- Slope = (-7 - (-3)) / (-3 - 3) = -4 / -6 = 2/3
For line DE:
- Coordinates D(6, -5) and E(0, 4)
- Slope = (4 - (-5)) / (0 - 6) = 9 / (-6) = -3/2
Comparing the slopes:
BC slope = 2/3
DE slope = -3/2
Since the slopes are different, BC and DE are not parallel.
To determine whether they are perpendicular or neither, we need to check if the product of their slopes is -1.
Product of BC slope (2/3) and DE slope (-3/2) = (2/3) * (-3/2) = -1
The product of the slopes is -1, so BC and DE are perpendicular lines.
Therefore:
- Line BC and line DE are not parallel.
- Line BC and line DE are perpendicular.