A group of friends are hiking on trail Y when they reach an intersection with trail X. Trail X is perpendicular to trail y If trail Y has a slope of -one half, which of the following statements are true? Trail X is steeper than trail Y. Trail X has a positive slope (it runs uphill). Trail X has a negative slope (it runs downhill Trail Y is steeper than trail X

Question

A group of friends are hiking on trail Y when they reach an intersection with trail X. Trail X is perpendicular to trail y If trail Y has a slope of -one half, which of the following statements are true? Trail X is steeper than trail Y. Trail X has a positive slope (it runs uphill).  Trail X has a negative slope (it runs downhill Trail Y is steeper than trail X

mww · Answer

If two lines are perpendicular, then the product of their gradients is -1. (m1 x m2 = -1)
We say the slopes are then negative reciprocals of each other so that m1 = -1/m2

Slope Y = -1/2
-1/2 (slope X) = -1
Slope X = -1/(-1/2) = 2

X is steeper because the absolute value of the slope is larger (ignoring the sign, the larger number represents steeper slope in either direction)