Testwiki:Reference desk/Archives/Mathematics/2016 April 5

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April 5

Vector proof

Given a Quadrilateral $ABCD$ and $E,F$ are midpoints of $AD,BC$ respectively,

Prove: $\overrightarrow{EF}=\frac{\overrightarrow{AB}+\overrightarrow{DC}}{2}$ . יהודה שמחה ולדמן (talk) 09:44, 5 April 2016 (UTC)

Please see our note at the top of the page regarding homework. What have you done so far and where are you stuck?

To start you out:

• Have you drawn a diagram of the problem?
• Do you know and understand why, given the points $W,X,Y,Z$, then $\overrightarrow{WZ}=\overrightarrow{WX}+\overrightarrow{XY}+\overrightarrow{YZ}$?
• How many ways can you represent $\overrightarrow{EF}$ in terms of vectors not utilizing the points $E,F$?
• Can you think of a way to combine those equations so that you can solve for $\overrightarrow{EF}$ in the desired terms?

Our relevant article is Vector addition. -- ToE 14:07, 5 April 2016 (UTC)