Math Snap

STEP 1

Assumptions1. Triangle R is given.
. U lies on line TS with TUUS =3.
3. M is the midpoint of line RU.
4. Ray TM intersects line RS at V.

STEP 2

Since M is the midpoint of RU, we can say that RMMU =11.

STEP 3

Since U lies on line TS with TUUS =23, we can say that RTTS =23.

STEP 4

Now, we can use the section formula (also known as the ratio theorem) to find the ratio RVVS. The section formula states that if a point divides a line segment in the ratio m:n, then the ratio of the distances from the point to the ends of the line segment is n:m.
$$RVVS = (RM \times US + MU \times RS) (RM \times TS + MU \times RT)$$

STEP 5

Substitute the given ratios into the formula.
$$RVVS = ((1 \times3) + (1 \times RS)) ((1 \times2) + (1 \times RT))$$

STEP 6

implify the equation.
$$RVVS = (3 + RS) (2 + RT)$$

STEP 7

Since RS and RT are parts of the same line, we can say that RS = RT. So, we can substitute RS for RT in the equation.
$$RVVS = (3 + RS) (2 + RS)$$

STEP 8

Since both terms in the ratio contain RS, we can cancel it out.
$$RVVS =32$$

Since V lies on line RS, we can say that RVVS = RVRS.
Therefore, RVRS =32.