Question

Let $A=(a_1,a_2)\text{and}B=(b_1,b_2)$ be two points in the plane with integer coordinates. Which one of the following is not a possible value of the distance between $A$ and $B?$

• A. $\sqrt{65}$
• B. $\sqrt{74}$
• C. $\sqrt{83}$
• D. $\sqrt{97}$

Answer 1

The correct option is C $\sqrt{83}$

Using distance formula
$AB=\sqrt{(a_1-b_1{)}^2+(a_2-b_2{)}^2}$

Option a) $AB=\sqrt{8^2+1^2}=\sqrt{65}\text{(possible)}$

Option b) $AB=\sqrt{7^2+5^2}=\sqrt{74}\text{(possible)}$

Option c) $AB=\sqrt{83}\text{(not possible)}$

Option d) $AB=\sqrt{9^2+4^2}=\sqrt{97}\text{(possible)}$


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