Question

how are lines kl and mn related?
○ the lines intersect at point k.
○ the lines are parallel.
○ the lines are perpendicular.
○ the lines do not have slopes.

Explanation:

1. Analyze line KL: It's a horizontal line (parallel to the x - axis), so its slope is 0 (since for a horizontal line \(y = c\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=0\) as \(y_2=y_1\)).
2. Analyze line MN: It's a vertical line (parallel to the y - axis), so its slope is undefined (since for a vertical line \(x = c\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\) and \(x_2=x_1\), leading to division by zero).
3. Recall the property of perpendicular lines: A horizontal line (slope 0) and a vertical line (undefined slope) are perpendicular to each other. Also, check the intersection: Line KL (horizontal) and line MN (vertical) intersect at point P, not K. They are not parallel (one has slope 0, the other undefined). And both have slopes (0 for KL, undefined for MN), so the correct relation is that they are perpendicular.

Answer:

The lines are perpendicular.