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Show that the triangle formed by the points(4,4),(3,5) and (-1,-1) is a right angled traingle.

Let the given points be A,B,C are the vertices of the given triangle.

Now finding the distance between the vertices or the length of the sides,

{\bar  A}B={\sqrt  {(4-3)^{2}+(4-5)^{2}}},{\bar  B}C={\sqrt  {(3+1)^{2}+(5+1)^{2}}},{\bar  C}A={\sqrt  {(-1-4)^{2}+(-1-4)^{2}}}\,

{\bar  A}B={\sqrt  {2}},{\bar  B}C={\sqrt  {52}},{\bar  C}A={\sqrt  {50}}\,

The realation among the three sides is like

({\bar  B}C)^{2}=({\bar  A}B)^{2}+({\bar  C}A)^{2}\,

This is the essential condition of a right angled triangle.

Hence the given points form the vertices of a right angled traingle.

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