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.
graph: coordinate plane with horizontal line kl (through k(-8,2), p(-4,2), l(6,2)) and vertical line mn (through m(-4,8), p(-4,2), n(-4,-6)) intersecting at p

Explanation:

1. Analyze line KL: Line KL is horizontal (parallel to the x - axis). The slope of a horizontal line is calculated using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. For two points on KL, say $K(-8,2)$ and $L(6,2)$ (assuming the y - coordinate is 2 from the graph), $m_{KL}=\frac{2 - 2}{6-(-8)} = 0$.
2. Analyze line MN: Line MN is vertical (parallel to the y - axis). For a vertical line, the slope is undefined because if we take two points on MN, say $M(-6,8)$ and $N(-6, - 6)$, the slope formula gives $m_{MN}=\frac{-6 - 8}{-6-(-6)}=\frac{-14}{0}$, which is undefined.
3. Recall the relationship between horizontal and vertical lines: A horizontal line (slope = 0) and a vertical line (slope undefined) are perpendicular to each other.
4. Evaluate other options:

• The lines do not intersect at point K (KL is horizontal, MN is vertical, they intersect at point P).
• The lines are not parallel (one has slope 0, the other has undefined slope, parallel lines have equal slopes).
• Both lines have slopes (KL has slope 0, MN has an undefined slope, so the statement "The lines do not have slopes" is wrong).

Answer:

The lines are perpendicular.