Let Delta ABC be a nondegenerate triangle and let f be a mot

Let Delta ABC be a nondegenerate triangle and let f be a motion of the plane such that f(A) = A, f(B) = B and f(C) = C. Show that f is the identity: that is, f(x) = x for any point X on the plane.

Solution

Given the triangle is nondegenerate triangle ,so the vertices looks like they are lying on same line.

It is given that the motion of the plane is such that f(A)=A ,f(B)=B and f(C)=C.

So the motion of plane should be such that it should rotate about that axis that CONTAIN A,B,C .

Hence, for every point on that axis f(X)=X.

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