Question

$ABCD$ is parallelogram. If $L$ and $M$ are the middle points of $BC$ and $CD$, then $ \overrightarrow {AL}+ \overrightarrow {AM}= $

• A. $ \dfrac { 1 }{ 2 } \overrightarrow{AC}$
• B. $ \dfrac { 3 }{ 2 } \overrightarrow{AC}$
• C. $\overrightarrow{AC}$
• D. None of the above

Answer 1

The correct option is B $ \dfrac { 3 }{ 2 } \overrightarrow{AC}$

$AL=AB+BL=AB+\frac{1}{2}BC=AB+\frac{1}{2}AD$

$AM=AD+DM=AD+\frac{1}{2}DC=AD+\frac{1}{2}AB$

Adding, $AL+AM=\frac{3}{2}(AB+AD)=\frac{3}{2}(AB+BC)=\frac{3}{2}AC$