# Finding the transformation matrix to transform one triangle into another

I have 2 sets of 3 points: the "origin" and "destiny". Any ideas on how to find the best-fit transformation matrix that will convert the origin's points to destiny using (only) rotation, scaling and translation?

I know a way to solve that, which is creating a function that applies the 3 transformation to the origin points and calculate the distance of them to the destiny points; then I minimize this function. Any easier way?

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For instance, a) apply a translation to move the point in the first pair to the origin; b) apply a rotation about an axis through the origin to move the point in the second pair onto the $z$-axis; c) apply a rotation about the $z$-axis to move the point in the third pair into the $y$-$z$-plane with non-negative $y$ coordinate. That moves all congruent triangles with identically numbered points into the same position.