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:

Step1: Calculate the slope of line KL

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For line \(KL\), assume \(K(-6,2)\) and \(L(4,2)\). Then \(m_{KL}=\frac{2 - 2}{4-(-6)}=\frac{0}{10} = 0\) (horizontal line).

Step2: Calculate the slope of line MN

For line \(MN\), assume \(M(-4,6)\) and \(N(-4,-6)\). Then \(m_{MN}=\frac{-6 - 6}{-4-(-4)}=\frac{-12}{0}\) (undefined, vertical line).

Step3: Analyze the relationship

A horizontal line (\(m = 0\)) and a vertical line (undefined slope) are perpendicular.

Answer:

The lines are perpendicular.