Find all values of y such that the distance between (5,y) and (-7,2) is 18.
Remember that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]substitute the given values
[tex]18=\sqrt[]{(y-2)^2+(5+7)^2}[/tex][tex]18=\sqrt[]{(y-2)^2+144}[/tex]squared both sides
[tex]18^2=(y-2)^2+144[/tex]solve for y
[tex]\begin{gathered} (y-2)^2=324-144 \\ (y-2)^2=180 \end{gathered}[/tex]take square root on both sides
[tex]\begin{gathered} y-2=\pm\sqrt[]{180} \\ y=2\pm\sqrt[]{180} \end{gathered}[/tex]simplify
[tex]y=2\pm6\sqrt[]{5}[/tex]