Question

Choose which lines are perpendicular. After doing the necessary work, circle your final answer. Line p passes through (4, 0) and (6, 4) Line q passes through (0, 4) and (6, 4) Line r passes through (0, 4) and (0, 0) Item 6 Item 7 Item 8 Item 9 (1 point) Line p and line q Line p and line r None of These Line q and line r < <

Answer 1

To determine which lines are perpendicular, we first need to find the slopes of the lines. Two lines are perpendicular if the product of their slopes is -1.

1. **Line p:** passes through points (4, 0) and (6, 4).

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 0}{6 - 4} = \frac{4}{2} = 2
\]

2. **Line q:** passes through points (0, 4) and (6, 4).

\[
\text{slope} = \frac{4 - 4}{6 - 0} = \frac{0}{6} = 0
\]

3. **Line r:** passes through points (0, 4) and (0, 0).

As this line is vertical, the slope of line r is undefined.

Now, we analyze the slopes:
- Line p has a slope of 2.
- Line q has a slope of 0 (horizontal line).
- Line r is vertical with an undefined slope.

Next, we check for perpendicularity:
- The product of the slopes of lines p and q:
\[
2 \times 0 = 0 \quad \text{(not perpendicular)}
\]

- Line p (slope of 2) and line r (undefined slope) are perpendicular because a vertical line is always perpendicular to a horizontal line.

- Line q (slope of 0) and line r (undefined slope) are also perpendicular because, again, a vertical line is always perpendicular to a horizontal line.

**Final answer:**
Line p and line r are perpendicular. Also, line q and line r are perpendicular.

So the answer is **Line q and line r** would also work. Since you have to choose one and they are asking to circle the final answer:

**Circle: Line q and line r.**