the medians of $\triangle pqr$ are $\overline{pt}$, $\overline{qu}$, and $\overline{rs}$. they meet at a single point $v$.
(in other words, $v$ is the centroid of $\triangle pqr$.)

suppose $qu = 21$, $pv = 18$, and $vs = 7$.
find the following lengths.
note that the figure is not drawn to scale.

$rs = $
$qv = $
$vt = $

Question

the medians of $\triangle pqr$ are $\overline{pt}$, $\overline{qu}$, and $\overline{rs}$. they meet at a single point $v$.
(in other words, $v$ is the centroid of $\triangle pqr$.)

suppose $qu = 21$, $pv = 18$, and $vs = 7$.
find the following lengths.
note that the figure is not drawn to scale.

$rs = $
$qv = $
$vt = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Centroid Theorem", "Triangle Medians" ], "new_concepts": [], "current_concepts": [ "Centroid Theorem", "Triangle Medians" ] } ## Calculate RS using the Centroid Theorem $$ \begin{aligned} &RV = 2 \cdot VS \ &VS = 7 \ &RV = 2 \cdot 7 = 14 \ &RS = RV + VS = 14 + 7 = 21 \end{aligned} $$ ## Calculate QV using the Centroid Theorem $$ \begin{aligned} &QV = \frac{2}{3} \cdot QU \ &QU = 21 \ &QV = \frac{2}{3} \cdot 21 = 14 \end{aligned} $$ ## Calculate VT using the Centroid Theorem $$ \begin{aligned} &PV = 2 \cdot VT \ &PV = 18 \ &VT = \frac{1}{2} \cdot PV = \frac{1}{2} \cdot 18 = 9 \end{aligned} $$ The medians of $\triangle PQR$ are $\overline{PT}$, $\overline{QU}$, and $\overline{RS}$. They meet at a single point $V$. Suppose $QU = 21$, $PV = 18$, and $VS = 7$. Find the following lengths. $RS =$ 21 $QV =$ 14 $VT =$ 9 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Centroid Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate RS using the Centroid Theorem

Calculate QV using the Centroid Theorem

Calculate VT using the Centroid Theorem

Answer: