Using Midpoint and Distance Formulas

We know that $\overline{S M}$ has the same length as $\overline{M P}$ because they have matching tick-marks. This means that $M$ is the midpoint of $\overline{S P} .$ Therefore, $M$ is the segment bisector.

Since

\overline{S M}

and

\overline{M P}

are the same, the expressions for their lengths must be equal. We can set the two expressions equal to one another and solve for

x .

7 x + 5 = 8 x

SubEqn

LHS - 7 x = RHS - 7 x

5 = x

RearrangeEqnRearrange equation

x = 5

The length of

\overline{S M}

is given by

7 x + 5 .

We can substitute

5

for

x

to find

S M .

S M = 7 x + 5

Substitute

x = 5

S M = 7 (5) + 5

MultiplyMultiply

S M = 35 + 5

AddTermsAdd terms

S M = 40

Using Midpoint and Distance Formulas 1.4 - Solution