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

Line KL is a horizontal line. The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a horizontal line, \(y_1=y_2\). Let's assume two points on KL, say \(K(-8,2)\) and \(L(6,2)\). Then \(m_{KL}=\frac{2 - 2}{6-(-8)}=\frac{0}{14} = 0\).

Step2: Calculate the slope of line MN

Line MN is a vertical line. For a vertical line, \(x_1=x_2\). Let's assume two points on MN, say \(M(-4,8)\) and \(N(-4,-6)\). Then \(m_{MN}=\frac{-6 - 8}{-4-(-4)}=\frac{-14}{0}\), which is undefined. A horizontal line (slope \(m = 0\)) and a vertical line (undefined slope) are perpendicular.

Answer:

The lines are perpendicular.