Slope and Perpendicular Segments

Slope and perpendicular segments

These exercises ask you to work with the slope of line segments and decide whether two segments are perpendicular.

1) Find the slope

If you know two points on a segment, use

[m = \frac{y_2 - y_1}{x_2 - x_1}]

Subtract the y-values and the x-values in the same order. Then simplify the fraction if possible.

2) Use perpendicular slope facts

Two non-vertical lines are perpendicular when their slopes are negative reciprocals. That means:

• one slope is (\frac{a}{b})
• the perpendicular slope is (-\frac{b}{a})

Special cases:

• a horizontal segment has slope 0, and a vertical segment is perpendicular to it
• a vertical segment has undefined slope

3) Compare or complete the work

Depending on the exercise, you may need to:

• compute a slope from coordinates
• decide whether two segments are perpendicular
• find a missing slope that makes segments perpendicular

4) Check your answer

Make sure the slope is simplified and the sign is correct. If you are checking perpendicularity, verify that the slopes multiply to (-1) when both slopes are defined.

Quick tip

Write the two points clearly and keep the order consistent. Many mistakes come from switching the subtraction order halfway through.