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Lines

Lines. Inclination of a Line. Similar to slope The inclination of a nonhorizontal line is the positive angle θ (less than π ) measured counterclockwise from the x-axis to the line. Which angle shows the inclination of the red line?. A. x-axis. D. B. C.

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Lines

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  1. Lines

  2. Inclination of a Line • Similar to slope • The inclination of a nonhorizontal line is the positive angle θ (less than π) • measured counterclockwise from the x-axis • to the line

  3. Which angle shows the inclination of the red line? A x-axis D B C

  4. Which angle shows the inclination of the red line? C x-axis D A B

  5. Inclination and Slope • If a nonvertical line has inclination θ • and slope m then • m = tan θ

  6. A few Problems • Find the slope of the line with the given inclination • θ = 3π/4 • θ = 2.88 • Find the inclination • of line with m = ¾ • of line through (6, 1) and (10, 8) • 6x – 2y + 8 = 0

  7. The Angle between Two Lines • Distinct lines??? • non parallel??? • non perpendicular??? • two pairs of angles • the acute pair is called the angle between two lines

  8. Angle between Two Lines • If two non perpendicular lines have slopes • m1 and m2, • The angle between the two lines is

  9. Find the angle between two lines • 2x – y – 4 = 0 and 3x + 4y – 12 = 0 • 3x + y – 3 = 0 and x – y – 2 = 0

  10. The Distance between a Point and a Line • The distance between a point (x1, y1) • and a line Ax + By + C = 0 is Find the distance between (4, 1) and the line y = 2x + 1 Find the distance between (2, 3) and the line 4x + 3y - 10

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