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The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.

User Svet Angelov
by
2.6k points

1 Answer

13 votes
13 votes

The points U, V, W and X all lie on the same line segment, in that order, such that the ratio of UV : VW:W X is equal to 1:3 : 4. If U X = 8, find VX.​

In this problem we have that

UV+VW+WX=UX -----> by addition segment postulate

we have

UX=8 units

so

UV+VW+WX=8 -------> equation A

UV/VW=1/3 ------> equation B

UV/WX=1/4 -----> equation C

Solve the system of equations

In equation B isolate the variable VW

so

3UV=VW

VW=3UV -------> equation D

In equation C isolate the variable WX

4UV=WX

WX=4UV ------> equation E

Substitute equation D and equation E in equation A

UV+(3UV)+(4UV)=8

solve for UV

8UV=8

UV=1

Find VW

VW=3UV

VW=3(1)=3 units

FInd WX

WX=4UV

WX=4(1)=4 units

Find out the value of VX

we have that

VX=VW+WX

substitute

VX=3+4=7 units

therefore

VX=7

User Frank Luke
by
2.6k points
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