Math Snap

STEP 1

Assumptions1. Point $$ is the midpoint of $\overline{RT}$.
. The length of segment $RS$ is $6y+3$.
3. The length of segment $$ is $3y+9$.

STEP 2

Since is the midpoint of $\overline{RT}$, the lengths of segments $RS$ and are equal. We can set up the equation $RS =$.
$$6y+ =y+9$$

STEP 3

To isolate $y$, we can subtract $3y$ from both sides of the equation.
$$6y -3y =3y+9 -3y$$This simplifies to$$3y +3 =9$$

STEP 4

Next, subtract3 from both sides of the equation to solve for $y$.
$$3y =9 -3$$This simplifies to$$3y =6$$

STEP 5

Finally, divide both sides of the equation by3 to find the value of $y$.
$$y = \frac{}{3}$$So, $y =2$.

STEP 6

Now, we can substitute $y =2$ back into the expressions for $RS$ and $$ to find their lengths.
For $RS$$$RS =6y+3 =6(2) +3$$

STEP 7

Calculate the length of $RS$.
$$RS =12 +3 =15$$

STEP 8

For $$$$ =3y+ =3(2) +$$

STEP 9

Calculate the length of $$.
$$=6 +9 =15$$

STEP 10

Finally, we can find the length of $\overline{RT}$ by adding the lengths of $RS$ and $$.
$$RT = RS + =15 +15$$

Calculate the length of $RT$.
$$RT =30$$So, $y =$, $RS =15$, and $RT =30$.