If R is the midpoint of segment QS, QR = 6x-61 and R = x-6, find the value of QS

Answer 1

R is the midpoint of QS,

QR=RS

6x-61 = x-6

6x-x = -6+61

5x = 55

x=55/5= 11

x= 11

RS = x-6=11-6= 5

QR = 6x-61 = 6(11)-61 = 66-61=5

QS = QR+RS = 5+5 = 10

QS =2QR = 2RS = 2(5)= 10

QS =10

Answer 2

By the definition of midpoint, the segments have to be of equal length. So you can set up an equation.

6x-61=x-6 Subtract x from both sides

6x-61-x=x-6-x Simplify

5x-61=-6 Add 61 to both sides

5x-61+61=-6+61 Simplify

5x=55 Divide both sides by 5

x=11

Now that we have x, can plug it in to find the value of QS

QR=6(11)-61 = 5

Since both halves are equal, the 5x2 = 10 for the total length of QS