QuestionIn , U divides in a ratio. M is the midpoint of . Find RV:RS.
Studdy Solution
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.
STEP 5
Substitute the given ratios into the formula.
STEP 6
implify the equation.
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.
STEP 8
Since both terms in the ratio contain RS, we can cancel it out.
STEP 9
Since V lies on line RS, we can say that RVVS = RVRS.
Therefore, RVRS =32.
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