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Line A y= 2x - 3

Line B y= 2x + 5
Line C y= -1/2x -2
Line D y= 1/2x + 2

Given the linear equations in the table, which of the following statements is true?

A. Line A is perpendicular to line B .
B. Line B is perpendicular to line D .
C. Line A is perpendicular to line C .
D. Line C is perpendicular to line D .

1 answer

To determine which of the statements is true regarding perpendicular lines, we need to look at the slopes of each line in the equations:

  1. Line A: \(y = 2x - 3\)
    Slope (m) = 2

  2. Line B: \(y = 2x + 5\)
    Slope (m) = 2

  3. Line C: \(y = -\frac{1}{2}x - 2\)
    Slope (m) = -\(\frac{1}{2}\)

  4. 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.