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

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Presentation transcript:

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

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

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

The angle between two lines. If two non-perpendicular lines have slopes m 1 and m 2, then the angle between the two lines is given by

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. m 1 = 2 and m 2 = -3/4 Now plug these into the equation. Now take the arctan of 11/2

The Distance Between a Point and a Line. The distance between the point (x 1, y 1 ) and the line given by Ax + By + C is

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

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

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).

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.