Concept explainers
Angle Between Two Lines In this exercise we find a formula for the angle formed by two lines in a coordinate plane.
- (a) If L is a line in the plane and θ is the angle formed by the line and the x-axis as shown in the figure, show that the slope m of the line is given by
- (b) Let L1 and L2 be two nonparallel lines in the plane with slopes m1 and m2, respectively. Let ψ be the acute angle formed by the two lines (see the following figure). Show that
- (c) Find the acute angle formed by the two lines
- (d) Show that if two lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other. [Hint: First find an expression for cot ψ.]
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Chapter 7 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
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