Question

Find all values of y such that the distance between (5,y) and (-7,2) is 18.

Answer 1

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

`d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}`

substitute the given values

`18=\sqrt[]{(y-2)^2+(5+7)^2}`
`18=\sqrt[]{(y-2)^2+144}`

squared both sides

`18^2=(y-2)^2+144`

solve for y

`\begin{gathered} (y-2)^2=324-144 \\ (y-2)^2=180 \end{gathered}`

take square root on both sides

`\begin{gathered} y-2=\pm\sqrt[]{180} \\ y=2\pm\sqrt[]{180} \end{gathered}`

simplify

`y=2\pm6\sqrt[]{5}`