Find the distance between the x-intercept and the y-intercept of the graph of the equation 2x-5y=10.
+26367 Find the distance between the x-intercept and the y-intercept of the graph of the equation \(2x-5y=10\).
\(\begin{array}{|rcll|} \hline 2x-5y &=& 10 \quad & | \quad : 10 \\\\ \dfrac{2x}{10}-\dfrac{5y}{10} &=& 1 \\\\ \dfrac{ x}{5}-\dfrac{ y}{2} &=& 1 \\\\ \mathbf{\dfrac{ x}{5}+\dfrac{ y}{-2}} &=& \mathbf{1} \\ \hline \end{array} \)
x-intercept \(= 5\)
y-intercept \(= -2\)
The distance:
\(\begin{array}{|rcll|} \hline && \sqrt{5^2+(-2)^2} \\ &=& \sqrt{25+4} \\ &=& \mathbf{\sqrt{29}} \\ \hline \end{array}\)
