Question

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

Explanation:

Step1: Determine 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 \(m_{KL}=0\).

Step2: Determine the slope of line MN

Line MN is a vertical line. For a vertical line \(x_1 = x_2\), and the slope formula results in division by zero. The slope of a vertical line is undefined. But we can also use the property of perpendicular lines: the product of slopes of two perpendicular lines \(m_1\times m_2=- 1\). A horizontal line (\(m = 0\)) and a vertical line (undefined slope in the sense of the \(y - x\) ratio, but geometrically) are perpendicular.

Answer:

The lines are perpendicular.