Math

QuestionFind WYW Y given WW is the midpoint of segment VYVY, where VW=9x+7V W=9 x+7 and WY=16x28W Y=16 x-28.

Studdy Solution

STEP 1

Assumptions1. Point W is the midpoint of Segment VY. . The length of segment VW is given by the expression 9x+79x +7.
3. The length of segment WY is given by the expression 16x2816x -28.

STEP 2

Since W is the midpoint of VY, the lengths of VW and WY are equal. We can set up an equation to represent this.
VW=WYVW = WY

STEP 3

Substitute the given expressions for VW and WY into the equation.
9x+7=16x289x +7 =16x -28

STEP 4

To solve for x, we need to isolate x on one side of the equation. Start by subtracting 9x9x from both sides of the equation.
7=7x287 =7x -28

STEP 5

Next, add28 to both sides of the equation to isolate 7x7x on one side.
35=7x35 =7x

STEP 6

Finally, divide both sides of the equation by to solve for x.
x=5x =5

STEP 7

Now that we have the value of x, we can substitute it back into the expression for WY to find the length of WY.
WY=16x28WY =16x -28

STEP 8

Substitute x=5x =5 into the expression.
WY=16(5)28WY =16(5) -28

STEP 9

Calculate the length of WY.
WY=8028=52WY =80 -28 =52The length of segment WY is52.

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