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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

3. Using Midpoint and Distance Formulas

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Exercise 4 Page 397

Segments RM and MS are congruent.

Segment Bisector: n
RS = 66

Practice makes perfect

We know that segment RM is congruent to MS because they have matching tick-marks. Therefore, the line that goes through the midpoint M is the segment bisector. This is line n.

Since RM and MS are congruent, the expressions for their lengths must be equal.

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

4x+3=6x-12

LHS-4x=RHS-4x

3=2x-12

LHS+12=RHS+12

15=2x

.LHS /2.=.RHS /2.

7.5=x

Rearrange equation

x=7.5

The length of RS is given by 4x+3+6x-12, the sum of RM and MS. We can simplify this expression and then substitute 7.5 for x to find RS.

RS=4x+3+6x-12

Add and subtract terms

RS=10x-9

x= 7.5

RS=10( 7.5)-9

Multiply

RS=75-9

Subtract term

RS=66

Subchapter links

Communicate Your Answer p.395

Monitoring Progress p.396-399

Exercises p.400-402