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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

3. Using Midpoint and Distance Formulas

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Exercise 9 Page 24

Segments XM and MY are congruent.

Segment Bisector: MN
XY=32

Practice makes perfect

We know that segment XM is congruent to MY because they have matching tick-marks. This means that M is the midpoint of XY. Therefore, the segment bisector is MN.

Since XM and MY are congruent, the expressions for their lengths must be equal.

We can set the two expressions equal to one another and solve for x.

3x+1=8x-24

LHS-3x=RHS-3x

1=5x-24

LHS+24=RHS+24

25=5x

.LHS /5.=.RHS /5.

5=x

Rearrange equation

x=5

The length of XY is given by 3x+1+8x-24, the sum of XM and MY. We can simplify this expression and then substitute 5 for x to find XY.

XY=3x+1+8x-24

Add and subtract terms

XY=11x-23

x= 5

XY=11( 5)-23

Multiply

XY=55-23

Subtract term

XY=32

Subchapter links

Communicate Your Answer p.19

Monitoring Progress p.20-23

Exercises p.24-26