Question

triangles distance and the pythagorean theorem what is the length of the diagonal of the rectangle? round your answer to the nearest hundredth, if necessary.

Explanation:

Step1: Find the horizontal and vertical distances

The horizontal distance \( a \) between \( x = - 6\) and \(x = 4\) is \(|4-(-6)|=10\). The vertical distance \(b = 0\) (since the \(y -\)coordinates of the two points are both \(-3\)). But wait, no - actually, if we consider the two vertical sides as part of a right - triangle (the horizontal side is the base, and the difference in \(x\) values gives the base length of the right - triangle for the diagonal calculation). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \((x_1,y_1)=(-6,-3)\) and \((x_2,y_2)=(4,-3)\).

Step2: Apply the distance formula

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Answer:

\(10\)