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

7) BC = 10

8) BD = 20

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