Question

Write a simplified expression for the length of line AC.

Write a simplified expression for the length of line QR.

AC=
QR=

Answer 1

Answer:

$AC=8x-1$

$QR=5y+20$

Step-by-step explanation:

We are given that

$AB=x+2$

$BC=7x-3$

$PQ=8y+5$

$PR=13y+25$

We have to find the value of AC and QR

$AC=AB+BC$ (segment addition property)

Substitute the value

Then, we get

$AC=x+2+7x-3=8x-1$

$PQ+QR=PR$  (segment addition property)

Substitute the values then we get

$8y+5+QR=13y+25$

$QR=13y+25-8y-5$

Using subtraction property of equality

$QR=5y+20$

Answer 2

The simplified expressions for the length of the line segment are :

• AC = 8x - 1
• QR = 5y + 20

• The line segment AC equals:

AC = AB + BC ;

AB = x+2 ; BC = 7x-3

AC = x + 2 + 7x - 3

AC = 8x - 1

• Line segment PR

PR = PQ + QR - - (1)

PR = 13y + 25 ; PQ = 8y + 5

From (1)

QR = PR - PQ

Hence,

QR = 13y + 25 - (8y + 5)

QR = 13y + 25 - 8y - 5

QR = 5y + 20

Therefore, the line segments are :

• AC = 8x - 1
• QR = 5y + 20

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