Example 1
Completion requirements
| Example 1 |
The point \(P(2, 5)\) is plotted on the Cartesian plane. Determine the length of the line segment from the origin to point \(P\). Round to the nearest hundredth.
In order to determine the length of this line segment, we can construct a right triangle by drawing a vertical line to the \(x\)-axis from point \(P\).
Now that you have a right triangle, you can calculate the length of the unknown side.
\(\begin{align}
r &= \sqrt {\left( {x^2 + y^2 } \right)} \\
r &= \sqrt {\left( {\left( 2 \right)^2 + \left( 5 \right)^2 } \right)} \\
r &= \sqrt {4 + 25} \\
r &= \sqrt {29} \\
r &= 5.385... \\
r &\doteq 5.39 \\
\end{align}\)
\(\begin{align}
r &= \sqrt {\left( {x^2 + y^2 } \right)} \\
r &= \sqrt {\left( {\left( 2 \right)^2 + \left( 5 \right)^2 } \right)} \\
r &= \sqrt {4 + 25} \\
r &= \sqrt {29} \\
r &= 5.385... \\
r &\doteq 5.39 \\
\end{align}\)