To determine which statements about the lines are true, we need to check the slopes of the lines involved. Two lines are perpendicular if the product of their slopes is -1.
Here are the slopes of the given lines from their equations:
- Line A: \( y = 2x - 3 \) (slope = 2)
- Line B: \( y = 2x + 5 \) (slope = 2)
- Line C: \( y = -\frac{1}{2}x - 2 \) (slope = -\frac{1}{2})
- Line D: \( y = \frac{1}{2}x + 2 \) (slope = \frac{1}{2})
Now, we can evaluate each statement:
a. Line A is perpendicular to line B.
- False, since both lines have the same slope (2).
b. Line C is perpendicular to line D.
- Evaluate the product of their slopes: \(-\frac{1}{2} \times \frac{1}{2} = -\frac{1}{4}\).
- False, since the product is not -1.
c. Line A is perpendicular to line C.
- Evaluate the product of their slopes: \(2 \times -\frac{1}{2} = -1\).
- True, since the product is -1.
d. Line B is perpendicular to line D.
- Evaluate the product of their slopes: \(2 \times \frac{1}{2} = 1\).
- False, since the product is not -1.
Thus, the only true statement is:
c. Line A is perpendicular to line C.