Question

Part 1. Identify where the red figure is a translation or a rotation of the black figure​

Answer 1

A 90 degree counter-clockwise rotation is being done on the black figure to get the red figure.

The algebraic rule for a 90 degree counter-clockwise rotation is $(x,y) \to (-y,x)$

For instance, the point C = (0,1) moves to C' = (-1,0), which is shown in the graph given and also you can use the rule above to get the same coordinates. The other points A,B and D follow the same rule.

Side note: the rotation is centered at the origin (0,0). This point is fixed.