Question

Points A, B, C, and D are collinear and positioned in that order. Find the length indicated 7) Find BC if BC = 2x + 4, AD = 28, CD = 3x - 2, and AB = 3x + 2. 8) Find BD if BD = -7 + 3x, AB = 2x - 14, AC = 2x - 3, and CD = 9.

Answer 1

Answer:

  7)  BC = 10

  8)  BD = 20

Step-by-step explanation:

7) The segment addition theorem tells you ...

  AB +BC +CD = AD

  (3x+2) +(2x+4) +(3x-2) = 28

  8x +4 = 28 . . . . collect terms

  8x = 24 . . . . . . . subtract 4

  x = 3 . . . . . . . . . divide by 8

  BC = 2x+4 = 2(3) +4

  BC = 10

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8) AB +BD = AC +CD

  (2x -14) +(-7 +3x) = (2x -3) +(9)

  5x -21 = 2x +6

  3x = 27

  x = 9

  BD = -7 +3x = -7 +3(9)

  BD = 20