Find Distance

Example on how to find the distance between a point and a midpoint.

Example 1

What is the distance between point C and the midpoint of segment AB?

graph_1


  1. $8$

  2. $2\sqrt{17}$

  3. $\sqrt{17}$

  4. $4\sqrt{17}$

  5. $4$

Solution


  1. We first determine the coordinates of all three points from the graph

    $A(-4,6)$ , $B(4,2)$ , $C(-2,-4)$

  2. We now calculate the midpoint $M$ of segment $AB$

    $(\dfrac{-4+4}{2},\dfrac{6+2}{2})=(0,4)$

  3. 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