Question

Use the following four coordinates to determine which one has a distance of 6 units from point E (3, 1). (5, 1) (2, 4) (3, 7) (7, 2)

Answer 1

Use the distance formula to find the distance between two points.
For any points $P(x_1,\ y_1)$ and $Q(x_2,\ y_2)$, the distance between them $PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$EA=\sqrt{(3-5)^2+(1-1)^2}=\sqrt{(-2)^2+0^2}=\sqrt{4}=2$
$EB=\sqrt{(3-2)^2+(1-4)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}$
$EC=\sqrt{(3-3)^2+(1-7)^2}=\sqrt{0^2+(-6)^2}=\sqrt{36}=6$
$ED=\sqrt{(3-7)^2+(1-2)^2}=\sqrt{(-4)^2+(-1)^2}=\sqrt{16+1}=\sqrt{17}$

The correct answer is C(3, 7).
(you don't even need to use the distance formula to realize this since it's 6 units directly above E(3, 1))