To determine which of the statements is true regarding perpendicular lines, we need to look at the slopes of each line in the equations:
-
Line A: \(y = 2x - 3\)
Slope (m) = 2 -
Line B: \(y = 2x + 5\)
Slope (m) = 2 -
Line C: \(y = -\frac{1}{2}x - 2\)
Slope (m) = -\(\frac{1}{2}\) -
Line D: \(y = \frac{1}{2}x + 2\)
Slope (m) = \(\frac{1}{2}\)
Lines are perpendicular if the product of their slopes is -1. Let's analyze the options:
A. Line A is perpendicular to line B.
Slope of A is 2 and slope of B is 2. \(2 \cdot 2 = 4 \neq -1\) (not perpendicular)
B. Line B is perpendicular to line D.
Slope of B is 2 and slope of D is \(\frac{1}{2}\). \(2 \cdot \frac{1}{2} = 1 \neq -1\) (not perpendicular)
C. Line A is perpendicular to line C.
Slope of A is 2 and slope of C is -\(\frac{1}{2}\).
\(2 \cdot -\frac{1}{2} = -1\) (perpendicular)
D. Line C is perpendicular to line D.
Slope of C is -\(\frac{1}{2}\) and slope of D is \(\frac{1}{2}\).
\(-\frac{1}{2} \cdot \frac{1}{2} = -\frac{1}{4} \neq -1\) (not perpendicular)
Thus, the true statement is:
C. Line A is perpendicular to line C.
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