Question

rectangle abcd has vertices at a(1,3), b(4,3), c(4,1), and d(1,1).
original coordinates rotated 90° counterclockwise around origin
a(-1,3) a(-3,-1)
b(-4,3) b(-3,-4)
c(-4,1) c(-1,-4)
d(-1,1) d(-1,-1)
describe how the coordinates changed.
each rotated x - coordinate is the opposite of the original? - coordinate.
each rotated y - coordinate is the same as the original? - coordinate.

Explanation:

Step1: Analyze the coordinate - transformation rule for 90 - degree counter - clockwise rotation

When a point \((x,y)\) is rotated 90 degrees counter - clockwise around the origin, the new coordinates \((x',y')\) are given by \((-y,x)\).
For point \(A(1,3)\), after 90 - degree counter - clockwise rotation, \(x'=-3\) and \(y' = 1\).

Step2: Determine the relationship between original and rotated coordinates

For the \(x\) - coordinate of the rotated point, it is the opposite of the original \(y\) - coordinate. For the \(y\) - coordinate of the rotated point, it is the same as the original \(x\) - coordinate.

Answer:

Each rotated \(x\) - coordinate is the opposite of the original \(y\) - coordinate.
Each rotated \(y\) - coordinate is the same as the original \(x\) - coordinate.