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.

Is this true or false?

Answer 1

The statement is True

Explanation:

If there are two non-vertical lines in the same plane and they intersect at a right angle then they are said to be perpendicular to each other. Horizontal and vertical lines are perpendicular to each other which means that the axes of the coordinate plane is perpendicular. The slopes of two perpendicular lines are negative reciprocals which simply means that for the product of the slopes to be -1, one of the slopes must be positive and the other negative.

Answer 2

Answer: It is true.

Explanation:

For example:

If the slope of a line "A" is 3/4 and it is perpendicular to a line "B", then the slope of the line B must be -4/3, because the slope of perpendicular lines are opposite reciprocal.

If you multiply this slopes, you obtain:

`((3)/(4))(-(4)/(3))=-1`

Therefore, keeping the explanation above on mind, the answer is: True.