Question 13

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waecmaths question: 

The coordinates of point P and Q are (4,3) and (2, –1) respectively. Find the shorest distance between P and Q

Option A: 

$10\sqrt{2}$

Option B: 

$4\sqrt{5}$

Option C: 

$5\sqrt{2}$

Option D: 

$2\sqrt{5}$

waecmaths solution: 

$\begin{align}  & ({{x}_{1}},{{y}_{1}})=(4,3) \\ & ({{x}_{2}},{{y}_{2}})=(2,-1) \\ & \left| PQ \right|=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}} \\ & \left| PQ \right|=\sqrt{{{(4-2)}^{2}}+{{[3-(-1)]}^{2}}} \\ & \left| PQ \right|=\sqrt{{{2}^{2}}+{{4}^{2}}}=\sqrt{4+16}=\sqrt{20} \\ & \left| PQ \right|=\sqrt{4\times 5}=2\sqrt{5} \\\end{align}$

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