Question

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.

Answer 1

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 = $\frac{615}{41}$

x = 15

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

                                      = 14(15) + 4

                                      = 214 units

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