In triangle ABC, D is the midpoint of BC. What is AB + AC?

Question 34

EasyOriginal question

In triangle $ABC$ , $D$ is the midpoint of $BC$ . What is $\overrightarrow{AB} + \overrightarrow{AC}$ ?

\overrightarrow{AD}

Correct answerYour answer

\overrightarrow{BC}

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2\overrightarrow{DA}

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2\overrightarrow{AD}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Taking $A$ as the origin, $D$ is the midpoint of $BC$ : $\overrightarrow{AD} = \frac{\overrightarrow{AB} + \overrightarrow{AC}}{2}$ .
So $\overrightarrow{AB} + \overrightarrow{AC} = 2\overrightarrow{AD}$ , twice the median.

Worth noting

$\overrightarrow{AD}$ forgets the half in the midpoint formula; the sum is twice the median.

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