Question below:

Question

For the point on the plane (8,−2), what are the coordinates of the point that will result from a translation of 4 units left and 2 units up, followed by a rotation of 90° counterclockwise about the origin?

Answer 1

Translating the point (8,2) 4 units left and 2 units up takes us to the point (8-4,-2+2) = (4,0).

A 90 degree counterclockwise rotation has the property of taking any point (a,b) to the point (-b, a). Therefore the point (4,0) would be taken to the point (0,4).

After a translation of 4 units left, 2 units up, followed by a 90 degree counterclockwise rotation, the point (8,-2) is taken to the point (0,4).