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.
-
Line p: passes through points (4, 0) and (6, 4).
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 0}{6 - 4} = \frac{4}{2} = 2 \]
-
Line q: passes through points (0, 4) and (6, 4).
\[ \text{slope} = \frac{4 - 4}{6 - 0} = \frac{0}{6} = 0 \]
-
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.
1 answer