In the coordinate plane, the points $F(-1,0)$, $G(2,3)$, and $H(5,0)$ lie on a circle with center $P$. What are the coordinates of point $P$?

เฉลยละเอียด

[STEP]Calculate the distance from $F$, $G$ and $H$ to each $P$ in the choices[/STEP]

The distance must be the same for the correct $P$.

Using the distance formula

$$\text{distance}=\sqrt{\Delta x^{2}+\Delta y^{2}}$$

The correct choice is (B) $(2,0)$

\begin{eqnarray*}
\overline{FP} & = & \sqrt{\left(-1-2\right)^{2}+\left(0-0\right)^{2}}=3\\
\overline{GP} & = & \sqrt{\left(2-2\right)^{2}+\left(0-3\right)^{2}}=3\\
\overline{HP} & = & \sqrt{\left(5-2\right)^{2}+\left(0-0\right)^{2}}=3
\end{eqnarray*}

[ANS]$P=(2,0)$[/ANS]

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