To determine which of the statements is true regarding the lines given in the table, we need to identify the slopes of each line since two lines are perpendicular if the product of their slopes is -1.
Let's extract the slopes from the equations:
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Line A: \(y = -12x - 2\)
- Slope (m) = -12
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Line B: \(y = 2x - 3\)
- Slope (m) = 2
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Line C: \(y = 12x + 2\)
- Slope (m) = 12
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Line D: \(y = 2x + 5\)
- Slope (m) = 2
Now let's check the pairs of lines:
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Line B (slope = 2) and Line D (slope = 2):
- Product of slopes: \(2 \times 2 = 4\) (not perpendicular)
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Line A (slope = -12) and Line B (slope = 2):
- Product of slopes: \(-12 \times 2 = -24\) (not perpendicular)
-
Line A (slope = -12) and Line C (slope = 12):
- Product of slopes: \(-12 \times 12 = -144\) (not perpendicular)
-
Line C (slope = 12) and Line D (slope = 2):
- Product of slopes: \(12 \times 2 = 24\) (not perpendicular)
Checking for perpendicular conditions:
Two lines are perpendicular if the product of their slopes equals -1. Here, no pair of lines has this property.
Result: None of the statements provided are true based on the criteria for perpendicular lines. However, we can identify that Line A and Line C have slopes that are negatives of each other. Hence, they are not perpendicular, but they can form a right angle under a different transformation.
In summary, all statements provided about the lines being perpendicular are incorrect. Please recheck the values given for the slopes if you're expecting a true statement among the options listed.