1 / 10

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.

monroem
Download Presentation

10.1 Lines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related