College Algebra, Chapter 2, 2.2, Section 2.2, Problem 10

Determine whether the points $(0,1), \left( \frac{1}{\sqrt{2}} ,\frac{1}{\sqrt{2}}\right)$ and $\left(\frac{\sqrt{3}}{2},\frac{1}{2} \right)$ are on the graph $x^2 +y^2 = 1$
@ point $(0,1)$

$
\begin{equation}
\begin{aligned}
0^2 + 1^2 &= 1\\
\\
1 &= 1
\end{aligned}
\end{equation}
$


@ point $\left( \frac{1}{\sqrt{2}} ,\frac{1}{\sqrt{2}}\right)$

$
\begin{equation}
\begin{aligned}
\left( \frac{1}{\sqrt{2}} \right)^2 + \left( \frac{1}{\sqrt{2}} \right)^2 &= 1 \\
\\
\left( \frac{1}{2} \right) + \left( \frac{1}{2} \right) &= 1\\
\\
\frac{2}{2} &= 1\\
\\
1 &= 1\\

\end{aligned}
\end{equation}
$


@ point $\left(\frac{\sqrt{3}}{2},\frac{1}{2} \right)$

$
\begin{equation}
\begin{aligned}
\left(\frac{\sqrt{3}}{2}\right)^2 + \left(\frac{1}{2}\right)^2 &= 1\\
\\
\frac{3}{4} + \frac{1}{4} &= 1 \\
\\
\frac{4}{4} &=1 \\
\\
1 &= 1
\end{aligned}
\end{equation}
$

It shows that all the given points satisfy the equation $x^2 + y^2 =1$

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