To determine which statements are true regarding the lines, we first need to identify the slopes of each line from their equations.
The slope-intercept form of a line is given by the equation \(y = mx + b\), where \(m\) represents the slope.
Here are the slopes for each line:
- Line A: \(y = -12x - 2\) → Slope = -12
- Line B: \(y = 2x - 3\) → Slope = 2
- Line C: \(y = 12x + 2\) → Slope = 12
- Line D: \(y = 2x + 5\) → Slope = 2
Next, we recall that two lines are perpendicular if the product of their slopes is equal to -1.
Now, we can evaluate the statements:
-
Line C is perpendicular to Line D:
- Slope of Line C = 12
- Slope of Line D = 2
- \(12 \times 2 \neq -1\) → Not true.
-
Line B is perpendicular to Line D:
- Slope of Line B = 2
- Slope of Line D = 2
- \(2 \times 2 \neq -1\) → Not true.
-
Line A is perpendicular to Line C:
- Slope of Line A = -12
- Slope of Line C = 12
- \(-12 \times 12 \neq -1\) → Not true.
-
Line A is perpendicular to Line B:
- Slope of Line A = -12
- Slope of Line B = 2
- \(-12 \times 2 = -24 \neq -1\) → Not true.
Based on the analysis, none of the provided statements are true. However, if I misunderstood the context of the question or if the range of possible responses was broader, please clarify, and I'll gladly reevaluate.
1 answer