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2.8 Distance from a Point to a Line

2.8 Distance from a Point to a Line. point ( x 1 , y 1 ). line equation: A x + B y + C = 0. (notice all on one side!). Distance from a point to a nonvertical line is Ex 1) Find distance between line & point (nearest hundredth) a) y = 3 x + 2 P(3, 4). 3 x – y + 2 = 0.

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2.8 Distance from a Point to a Line

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  1. 2.8 Distance from a Point to a Line

  2. point (x1, y1) line equation: Ax + By + C = 0 (notice all on one side!) Distance from a point to a nonvertical line is Ex 1) Find distance between line & point (nearest hundredth) a) y = 3x + 2 P(3, 4) 3x – y + 2 = 0

  3. Ex 1) Find distance between line & point (nearest hundredth) b) Line through (4, 2) and (–4, 5) and the point (4, 0) *have to find equation of line first!

  4. To find the distance between 2 parallel lines, simply find a point on one line first and then use the second line for equation Ex 2) Find the distance between parallel? yep! a point? How about (0, –3)

  5. These questions have lots of real world applicatons. Advice  Draw a picture! Ex 3) An aluminum awning has a wrought iron support bar attached to the building & the awning so that it is perpendicular to the awning. From the picture, determine the length of the support bar (to nearest tenth) point: (0, 7.4) (0, 9) (3, 8.25) equation: (0, 7.4) (wall)

  6. We can indirectly measure lengths of things like wells by using gravity constant & speed of sound Because of gravity: d = 16t12 (t1 = time down) Because of sound: d = 1100t2 (t2 = time of sound back up) so 16t12 = 1100t2 Total time: T = t1 + t2 or t2 = T – t1 substitute…. 16t12 = 1100(T – t1) 16t12 + 1100t1 – 1100T = 0

  7. Ex 4) A rock was dropped in a well. The total time T for the rock to reach the bottom of the well and the sound to travel back was 4.5s. Find the depth of the well to the nearest foot. 16t12 + 1100t1 – 1100(4.5) = 0 16t12 + 1100t1 – 4950 = 0 use quad. form. t1 = 4.24 or –72.99 so, d = 16t12 = 16(4.24)2 = 288 ft.

  8. d = ± 2 (why ±? • Abs value means it • can be +2 or –2) Ex 5) Find the equations of all lines parallel to 3x – 5y = 0 located 2 units from the line. so

  9. Homework #209 Pg 111 #1–9 all 12, 14, 16, 18, 20, 21, 24, 25, 28

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