Answer
$Q = \left( {1,8} \right)$
Work Step by Step
We have $A = \left( {2, - 1} \right)$, $B = \left( {1,4} \right)$, and $P = \left( {2,3} \right)$.
So, the components of $\overrightarrow {AB} $ is
$\overrightarrow {AB} = B - A = \left( {1,4} \right) - \left( {2, - 1} \right) = \left( { - 1,5} \right)$
Let $Q = \left( {x,y} \right)$. So, the components of $\overrightarrow {PQ} $ is
$\overrightarrow {PQ} = Q - P = \left( {x,y} \right) - \left( {2,3} \right) = \left( {x - 2,y - 3} \right)$
Two vectors are equivalent if and only if they have the same components. Thus, $\overrightarrow {PQ} $ is equivalent to $\overrightarrow {AB} $ if $\left( {x - 2,y - 3} \right) = \left( { - 1,5} \right)$. It follows that $Q = \left( {x,y} \right) = \left( {1,8} \right)$.
