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Chapter 2: Problem 30

Find the midpoint of each line segment with the given endpoints. $$(\sqrt{50},-6) \text { and }(\sqrt{2}, 6)$$

Short Answer

Expert verified
The midpoint of the line segment with endpoints \((\sqrt{50}, -6)\) and \((\sqrt{2}, 6)\) is \(\left( \frac{\sqrt{50}+ \sqrt{2}}{2},0\right)\).

Step by step solution

01

Identify the coordinates

The given endpoints are \((\sqrt{50}, -6)\) and \((\sqrt{2}, 6)\). Identify \(x_1, y_1 = \sqrt{50}, -6\) and \(x_2, y_2 = \sqrt{2}, 6\)
02

Apply the midpoint formula

Use the midpoint formula \(( (x_1+x_2)/2 , (y_1+ y_2)/2)\). We substitute our identified coordinates into the formula. This will give \( \left( \frac{\sqrt{50}+ \sqrt{2}}{2} , \frac{-6+ 6}{2}\right)\)
03

Simplify the coordinates

The coordinates simplify to \(\left( \frac{\sqrt{50}+ \sqrt{2}}{2} , 0\right)\)

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