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Example 1
What is the distance between point C and the midpoint of segment AB?
- $8$
- $2\sqrt{17}$
- $\sqrt{17}$
- $4\sqrt{17}$
- $4$
Solution
- We first determine the coordinates of all three points from the graph
$A(-4,6)$ , $B(4,2)$ , $C(-2,-4)$
- We now calculate the midpoint $M$ of segment $AB$
$(\dfrac{-4+4}{2},\dfrac{6+2}{2})=(0,4)$
- We now calculate the distance $d$ between points $C(-2,-4)$ and $M(0,4,)$.
$d=\sqrt{(-2-0)^2+(-4-4)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}$
Answer B
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