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P, Q, V, and K are collinear with V between K and P, and Q between V and K. If VP = 14x + 4, PK = x + 630, VQ = 17x + 6, and KQ = 11x + 5, solve for VP.

Sagot :

   If the points P, Q, V and K are collinear, they will follow the segment addition postulate.

Measure of segment VP will be 214 units.

   It's given in the question,

  • P, Q, V and K are collinear.
  • VP = 14x + 4
  • PK = x + 630
  • VQ = 17x + 6
  • KQ = 11x + 5

By segment addition postulate,

            KQ + VQ + VP = KP

Substitute the values in the expression,

(11x + 5) + (17x + 6) + (14x + 4) = x + 630

(11x + 17x + 14x) + (5 + 6 + 4) = x + 630

42x + 15 = x + 630

42x - x = 630 - 15

41x = 615

x = [tex]\frac{615}{41}[/tex]

x = 15

Therefore, measure of VP = (14x + 4)

                                           = 14(15) + 4

                                          = 214 units

Measure of segment VP will be 214 units.

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