Exercise 6 Page 306

In the diagram, we can see that D is the midpoint of VW and that UX is the perpendicular to VW through D. Therefore, UX is the perpendicular bisector of VW.

According to the Perpendicular Bisector Theorem, in a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In our case, U is the point on the perpendicular bisector and V and W are the endpoints. Therefore, according to the theorem, UV=UW.

Since UV=UW, we can write an equation to find x. UV= UW ⇒ 9x+1= 7x+13 Let's solve the equation for x.

9x+1=7x+13

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Solve for x

SubEqn

LHS-7x=RHS-7x

2x+1=13

SubEqn

LHS-1=RHS-1

2x=12

DivEqn

.LHS /2.=.RHS /2.

x=6

We can now find the value UW by substituting 6 for x in the corresponding expression.

UW=7x+13

Substitute

x= 6

UW=7(6)+13

Multiply

Multiply

UW=42+13

AddTerms

Add terms

UW=55