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kakasveta [241]
3 years ago
9

Find the midpoint of the segment with the given endpoints. D(1, 2) and E(5, –2)

Mathematics
1 answer:
andre [41]3 years ago
4 0
The formula is (x + x / 2, y + y / 2)
1 + 5 / 2 = 3
-2+2 / 2 = 0

the mid point is (3,0)
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Step-by-step explanation:

1.) Consider triangle AEH

AEH is a right angle triangle as ∠AEH = 90°

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Applying Pythagorean theorem

AE^{2} + EH^{2} = AH^{2}

substituting values as given in the question:

7^{2} +EH^{2}=(7\sqrt{3} )^{2}\\EH^{2}=(7\sqrt{3} )^{2}-7^{2} \\EH^{2}=98\\EH=\sqrt{98}\\EH=7\sqrt{2}

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CDF is a right angle triangle as ∠CDF = 90°

CF is the hypotenuse of the triangle.

Applying Pythagorean theorem

CD^{2} + DF^{2} = CF^{2}

substituting values as given in the question:

11^{2} +DF^{2}=(11\sqrt{3} )^{2}\\DF^{2}=(11\sqrt{3} )^{2}-11^{2} \\DF^{2}=242\\DF=\sqrt{242}\\DF=11\sqrt{2}

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