To determine whether two lines are perpendicular, we need to examine the relationship between their slopes. Specifically, two lines are perpendicular if and only if the product of their slopes is equal to [tex]\(-1\)[/tex].
Here's the step-by-step process:
1. Identify the slopes of Line [tex]\(A\)[/tex] and Line [tex]\(B\)[/tex].
- The slope of Line [tex]\(A\)[/tex] is given as [tex]\(6\)[/tex].
- The slope of Line [tex]\(B\)[/tex] is [tex]\( -\frac{1}{6} \)[/tex].
2. Calculate the product of the slopes:
[tex]\[
\text{slope}_A \times \text{slope}_B = 6 \times \left(-\frac{1}{6}\right)
\][/tex]
3. Multiply the slopes:
[tex]\[
6 \times \left(-\frac{1}{6}\right) = -1
\][/tex]
4. Compare the product of the slopes to [tex]\(-1\)[/tex]:
- Here, the product of the slopes is [tex]\(-1\)[/tex].
Based on this calculation, since the product of the slopes is [tex]\(-1\)[/tex], it confirms that Lines [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are indeed perpendicular.
Answer: Yes
