Previously you found that a 15-degree counterclockwise rotation centered at(2,1)sends the point(4,6)to another point (x, y) ≈ (2.638, 6.347). The diagram on the right shows the vector v in the same direction as vector [2,5], only with a different length. Similarly, the vector u is per- pendicular to v and a different length. Show how you can use (2,1)+v+u to find the rotated point (x,y).

Answer 1

The unit vector a in the direction of v is a=v/|v|
similarly for u, b=u/|u|
Now, let w be the vector from (2,1) to the new point. Then
w = (2.638, 6.347)-(2,1) = [0.638,5.347]
Draw a right triangle, such that
k(a+b) = w
so, (2,1)+k(v/|v| + u/|u|) = (2.638, 6.347)