Question

xz = \sqrt{(11 - 4)^2 + (4 - 8)^2}

Explanation:

Step1: Identify the distance formula

The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, we assume the points are \((11,8)\) and \((4,4)\) (correcting the likely typo in the expression, assuming it's \((11 - 4)^2+(8 - 4)^2\) inside the square root, maybe a writing error in the original).

Step2: Simplify the terms inside the square root

First, calculate \((11 - 4)=7\) and \((8 - 4)=4\) (correcting the original's \((4 - 8)\) to \((8 - 4)\) as distance is absolute, or maybe the points are \((4,4)\) and \((11,8)\)). Then \((11 - 4)^2=7^2 = 49\) and \((8 - 4)^2=4^2 = 16\).

Step3: Sum the squares

Add the two results: \(49+16 = 65\).

Step4: Take the square root

\(XZ=\sqrt{65}\approx 8.06\) (if we consider the corrected expression, assuming the original had a sign error in the second term's subtraction). If we take the original as \((11 + 4)^2+(4 - 8)^2\) (though that's less likely for distance), \((11 + 4)^2=225\), \((4 - 8)^2 = 16\), sum is \(241\), root is \(\sqrt{241}\approx15.52\), but the distance formula usually has subtraction for coordinates. So likely the first correction is right.

Answer:

If the correct expression inside the square root is \((11 - 4)^2+(8 - 4)^2\), then \(XZ=\sqrt{49 + 16}=\sqrt{65}\approx 8.06\). If we take the original (with possible typo) as \((11 + 4)^2+(4 - 8)^2\), then \(XZ=\sqrt{225+16}=\sqrt{241}\approx15.52\). But the standard distance formula uses subtraction, so the more probable value is \(\sqrt{65}\) (or approximately \(8.06\)).