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10.1 Lines

10.1 Lines. The Inclination of a nonhorizontal line is the positive angle theta measured counterclockwise from the x-axis to the line. Acute angle. Obtuse angle. If a nonvertical line has inclination theta and slope m, then m = tan. rise or opp. }. Run or adj.

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10.1 Lines

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  1. 10.1 Lines The Inclination of a nonhorizontal line is the positive angle theta measured counterclockwise from the x-axis to the line. Acute angle Obtuse angle

  2. If a nonvertical line has inclination theta and slope m, then m = tan rise or opp. } Run or adj.

  3. Find the inclination of the line given by 2x + 3y = 6 First, find the slope by solving for y. Set m = tan -33.69o + 180o = 146.31o , the angle of inclination.

  4. The angle between two lines. If two non-perpendicular lines have slopes m1 and m2 , then the angle between the two lines is given by

  5. Find the angle between the two lines. Line 1: 2x - y - 4 = 0 Line 2: 3x + 4y -12 = 0 First, find the slope of the two lines. Now plug these into the equation. m1 = 2 and m2 = -3/4 Now take the arctan of 11/2

  6. The Distance Between a Point and a Line. The distance between the point (x1, y1) and the line given by Ax + By + C is

  7. Find the distance between the point (4,1) and the line y = 2x + 1 Note: first put the equation in general form. -2x + y - 1 = 0

  8. Find the area of a triangle with the points A(-3,0), B(0,4), C(5,2). B (0, 4) h C (5, 2) A (-3, 0) First, find the height.

  9. To find the height, we need to find the equation of line AC. So, find the slope of AC. Point-slope form gives us: Put this eq. in general form. x - 4y + 3 = 0 Now find h using this equation and the point (0,4).

  10. Now, using the distance formula between two points, find the length of base AC. Now, the area of a triangle is A = 1/2 (bh) So go ahead and find the area.

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