Exercise 19 Page 24

Practice makes perfect

a Since A is the midpoint of the segment XY, it divides XY into two congruent segments XA and AY.

This means that their lengths are equal. XA=AY Let's substitute the given expressions into our equation to find the value of x.

XA = AY

SubstituteII

XA= 3x, AY= 5x-6

3x= 5x-6

SubEqn

LHS-5x=RHS-5x

- 2x = - 6

DivEqn

.LHS /(- 2).=.RHS /(- 2).

x=3

Now, we can substitute x into the expression for XA.

XA = 3x

Substitute

x= 3

XA=3( 3)

Multiply

XA=9

b From Part A, we know that XA and AY are equal. Therefore, we know that AY is also equal to 9.

Since all of the points are on a straight line, we can form an equation for the total length using the Segment Addition Postulate. This postulate tells us that the total length XY is the sum of XA and AY. XY=XA+AY ⇒ 9+9=18

Subchapter links

Lesson Check p.23

Practice and Problem-Solving Exercises p.24-25

Standardized Test Prep p.26

Mixed Review p.26

Exercise 19 Page 24

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