Exercise 28 Page 393

Practice makes perfect

a The length

A C

is the total length of the segment,

\overline{A C} .

Because point

B

is on a straight line between

A

and

C,

we can use the Segment Addition Postulate to write an expression for the total length. We will add the lengths

A B

and

B C .

A C = A B + A C

SubstituteII

$A B = x + 2$ , $B C = 7 x - 3$

A C = (x + 2) + (7 x - 3)

RemovePar

Remove parentheses

A C = x + 2 + 7 x - 3

AddSubTerms

Add and subtract terms

A C = 8 x - 1

We can express the length

A C

8 x - 1 .

b We know the total length of

P R

and the length of the first segment,

P Q .

We need to figure out an expression for the second partial segment length,

Q R .

Since all the points are on a straight line, we can form an equation for the total length. The Segment Addition Postulate tells us that the total length

P R

is the sum of

P Q

and

Q R .

P R = P Q + Q R

SubstituteII

$P R = 13 y + 25$ , $P Q = 8 y + 5$

13 y + 25 = (8 y + 5) + Q R

RemovePar

Remove parentheses

13 y + 25 = 8 y + 5 + Q R

SubEqn

$LHS - 8 y = RHS - 8 y$

5 y + 25 = 5 + Q R

SubEqn

$LHS - 5 = RHS - 5$

5 y + 20 = Q R

RearrangeEqn

Rearrange equation

Q R = 5 y + 20

The length

Q R

can be expressed as

5 y + 20 .

Subchapter links

Communicate Your Answer p.387

Monitoring Progress p.388-391

Exercises p.392-394

Exercise 28 Page 393

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