Pre-Calc Exam Notes 33

Pre-Calc Exam Notes 33 - Rotations and Reflections of...

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Unformatted text preview: Rotations and Reflections of Angles • Section 1.5 33 Example 1.26 Recall that any nonvertical line in the xy-coordinate plane can be written as y = mx + b , where m is the slope of the line (defined as m = rise run ) and b is the y-intercept , i.e. where the line crosses the y- axis (see Figure 1.5.2(a)). We will show that the slopes of perpendicular lines are negative reciprocals. That is, if y = m 1 x + b 1 and y = m 2 x + b 2 are nonvertical and nonhorizontal perpendicular lines, then m 2 =− 1 m 1 (see Figure 1.5.2(b)). x y y = mx + b b run rise m = rise run (a) Slope of a line x y y = m 1 x + b 1 b 1 y = m 2 x + b 2 b 2 (b) Perpendicular lines Figure 1.5.2 First, suppose that a line y = mx + b has nonzero slope. The line crosses the x-axis somewhere, so let θ be the angle that the positive x-axis makes with the part of the line above the x-axis, as in Figure 1.5.3. For m > 0 we see that θ is acute and tan θ = rise run = m ....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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