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

= 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)