Question 1009174
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Show that the point (6,6), (2,3) and (4,7) are the vertices of a right angled triangle.
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Calculate the three segments in the coordinate plane that are sides of the triangle.

For example, one segment, connecting the points (6,6) and (2,3), is (6-2,6-3) = (4,3).
Its length is {{{sqrt(4^2 + 3^2)}}} = {{{sqrt(25)}}} = 5.

Two other segments are (2,-1) and (2,4).
Their lengths are {{{sqrt(2^2 + (-1)^2)}}} = {{{sqrt(5)}}} and {{{sqrt(2^2 + 4^2)}}} = {{{sqrt(20)}}}.

Now notice that {{{5^2}}} = 25 and {{{(sqrt(5))^2}}} + {{{(sqrt(20))^2}}} = 5 + 20 = 25.

It is just enough to state that the triangle is right-angled.
The point (4,7) is the vertex of the right angle.
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