Question

Identify the segment bisector of RS. Then find RS

Answer 1

The segment bisector of RS is M.

RS = 32

Explanation:

The segment bisector of RS is Point M since RM ≅ MS hence the congruency lines.

Since Point M is the bisector of RS, we know that RM = MS. We can then form the equation:

`RM =MS\\RM+MS=RS\\\\6x-2=3x+7\\3x-2=7\\3x=9\\x=3\\\\RM=6x-2\\RM=6(3)-2\\RM=18-2\\RM=16\\\\MS=3x+7\\MS=3(3)+7\\MS=9+7\\MS=16\\\\RM+MS=RS\\16+16=RS\\32=RS\\RS=32`

Answer 2

RS = 32

Explanation:

M is the bisector of RS , then

RM = MS , that is

6x - 2 = 3x + 7 ( subtract 3x from both sides )

3x - 2 = 7 ( add 2 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

Then

RS = 6x - 2 + 3x + 7 = 9x + 5 = 9(3) + 5 = 27 + 5 = 32