Step-by-step answer:
90 degree rotations, or multiples thereof, can be done by mapping the coordinates or by graphing.
In math, a positive rotation is counter-clockwise, if not specified. If specified, follow the specified direction.
By graphing, one would reproduced the same shape through the specified angle, by common sense.
On the other hand, I prefer to do rotations mathematically, and use common sense to check if the rotation has been done correctly.
Here are the rules for rotations of multiples of 90 degrees:
(x,y)=>(-y,x) [ 90 degrees, swap x, y, switch sign of the "new" x value]
(x,y)=>(-x,-y) [180 degrees]
(x,y)=>(y,-x) [270 degrees, or -90 degrees]
To see how it works, point (x,y) => (-y,x) when rotated 90 degrees.
To get 180 degrees rotation, we would rotate (-y,x) but using the rule of 90 degrees, so
(-y,x) => swap x, y, switch sign of the "new" x value
=> (x,-y) after swapping x, y. now switch the sign of "new" x to get (-x,-y)
which is the rotation of 180 degrees, or 2 times rotating 90 degrees.
Now get back to the problem at hand, the coordinates of the object are:
(0,-2)
(0,-3)
(1,-3)
(1,-5)
(3,-5)
(3,-4)
(2,-4)
(2,-3)
(3,-3)
(3,-2)
(0,-2)
We will take first (0,-2) using the rule
1. swap x,y switch sign of "new" x.
(0,-2) =>(-2,0) => (2,0) in the two given steps.
Now let's try (0,-3), similarly
(0,-3) =>(-3,0) => (3,0)
For (1,-3), we get
(1,-3) => (-3,1) => (3,1)
For (1,-5), we get
(1,-5)=> (-5,1) =>(5,1)
If we continue, this is what we'd get for a +90 rotation
(0,-2)=>(2,0)
(0,-3)=>(3,0)
(1,-3)=>(3,1)
(1,-5)=>(5,1)
(3,-5)=>(5,3)
(3,-4)=>(4,3)
(2,-4)=>(4,2)
(2,-3)=>(3,2)
(3,-3)=>(3,3)
(3,-2)=>(2,3)
(0,-2)=>(2,0) as in the first point.
Plot the points out and check if you get back the same shape, but rotated 90 degrees!
If you need further explanations, do not hesitate to post.
(If I am not available to answer, I am sure someone else would be able to help)