Question

The product of the slopes of two non-vertical perpendicular lines is always -1. It is NOT possible for two perpendicular lines to both have a positive slope because the product of two positives is positive. So for the product of the slopes to be -1, one of the slopes must be positive and the other negative.

T or F

Answer 1

I think the answer is true

Answer 2

Answer:

True.

Step-by-step explanation:

The given statement is true, because the condition of perpendicularity is

$m_{1} m_{2} =-1$

Where $m_{1}$ and $m_{2}$ are the slopes of the lines.

If you think this through, two perpendicular lines actually have inverse directions, because one must be horizontal regarding the direciton of the other.

So, that "opposite direction" is shown by having an opposite slope, which must also have opposite sign, because remember that signs represents the orientation of the line.

For example, if the first line has slope of 3, the perpendicular line must have a slope of -1/3, which completes the result -1.

Therefore, the statement is completely true.