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Find the distance between the x-intercept and the y-intercept of the graph of the equation 2x-5y=10.

 Mar 16, 2020
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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:

\(\begin{array}{|rcll|} \hline && \sqrt{5^2+(-2)^2} \\ &=& \sqrt{25+4} \\ &=& \mathbf{\sqrt{29}} \\ \hline \end{array}\)

 

laugh

 Mar 16, 2020

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