Given triangle ABC with vertices at points A( 1, 3 ), B( 5, 3 ), and C( 2, 5 ) and if the triangle is rotated 90° clockwise about the point ( 6, 1 ), find the new coordinates of  A'.

To find the new coordinates of A' after a 90° clockwise rotation about the point (6,1), we can use the formula for 2D rotation:

The formula for a 90° clockwise rotation about the origin (0,0) is (x', y') = (y, -x). However, since we are rotating about the point (6,1), we first need to shift the point A(1,3) by subtracting the rotation point from it. This gives us a shifted point A1(-5,2).

Now we can apply the rotation formula to A1. This gives us A2(2,5).

Finally, we shift A2 back by adding the rotation point to it. This gives us the final coordinates of A'(8,6).

To find the new coordinates of A' after a 90° clockwise rotation about the point (6,1), we can use the formula for 2D rotation:

The formula for a 90° clockwise rotation about the origin (0,0) is:

x' = y y' = -x

However, since we are rotating about the point (6,1) and not the origin, we first need to shift the point A(1,3) by subtracting the rotation point from it:

Shifted A = A - rotation point = (1-6, 3-1) = (-5, 2)

Now we can apply the rotation formula to the shifted A:

A' = (2, 5)

Finally, we shift A' back by adding the rotation point to it:

Final A' = A' + rotation point = (2+6, 5+1) = (8, 6)

So, the new coordinates of A' after a 90° clockwise rotation about the point (6,1) are (8, 6).