SOLUTION: Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the midpoint of the hypotenuse of the right triangle with vertices (0, 0), (5,0), and (0, 7) is equi

Question 1048897: Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the midpoint of the hypotenuse of the right triangle with vertices (0, 0), (5,0), and (0, 7) is equidistant from the three vertices.

Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the midpoint of the hypotenuse of the right triangle with vertices (0, 0), (5,0), and (0, 7) is equidistant from the three vertices.
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The hypotenuse is the line seqment that joins (5,0) and (0,7)
Its midpoint is (5/2,7/2)
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dist from (0,0) to (5/2,7/2):: sqrt[(5/2)^2 + (7/2)^2] = sqrt(18.5) = 4.3
dist from (5,0) to (5/2,7/2):: sqrt[(5-(5/2))^2 + (7/2)^2] = sqrt(18.5) = 4.3
dist from (0,7) to (5/2,7/2):: sqrt[(5/2)^2+ 3.5^2] = sqrt(18.5) = 4.3
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Cheers,
Stan H.
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Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the midpoint of the hypotenuse
of the right triangle with vertices (0, 0), (5,0), and (0, 7) is equidistant from the three vertices.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

It is true for any right angled triangle and the point that bisect the hypotenuse.

In a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse.

See the lesson
    - Median drawn to the hypotenuse of a right triangle
in this site.

There is this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this textbook under the topic Properties of triangles".

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