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: Find 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 \(y_1=y_2\), so \(m_{KL}=\frac{y - y}{x_2 - x_1}=0\).

Step2: Find the slope of line MN

Line MN is a vertical line. For a vertical line \(x_1 = x_2\), and the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) results in division by zero. A vertical line has an undefined slope. But we can also use the property of perpendicular lines: the product of slopes of two perpendicular lines \(m_1\times m_2=- 1\). Since \(m_{KL} = 0\) (horizontal line) and \(m_{MN}\) is undefined (vertical line), they are perpendicular.

Answer:

The lines are perpendicular.