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Chapter 1: Problem 107

Is it possible for two lines with positive slopes to be perpendicular? Explain.

Short Answer

Expert verified
No, two lines with positive slopes cannot be perpendicular because the slope of a line perpendicular to a positive slope would have to be negative.

Step by step solution

01

Understand the concept of slope

The slope of a line measures its steepness. It is usually represented by 'm' and is given by the ratio of vertical change to horizontal change between any two points on the line.
02

Applying perpendicular concept

In Euclidean geometry, two lines are perpendicular if they intersect at a 90-degree angle. The slopes of two perpendicular lines are negative reciprocals of each other. This means if a line has slope m, then the slope of the line perpendicular to it is -1/m.
03

Applying positive slope concept

We are given in the problem that the lines have positive slopes. The slope is positive if the line rises from left to right.
04

Final conclusion

If two lines with positive slopes are perpendicular, this would mean one has slope m and the other has slope of -1/m. But -1/m would be a negative slope, which contradicts our original assumption that both slopes are positive. Thus two lines with positive slopes cannot be perpendicular.

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