Question

Rotate ABC 90 degrees(counterclockwise) about the origin to create A'B'C what are the coordinates of the following point?
A(5,-1)
B(5,-9)
C(2,-7)

Answer 1

To rotate points counterclockwise by 90 degrees about the origin, you can use the following transformation for each point \((x, y)\):

\[
(x', y') = (-y, x)
\]

Now we will apply this transformation to each point:

1. For point \(A(5, -1)\):
- \(A' = (-(-1), 5) = (1, 5)\)

2. For point \(B(5, -9)\):
- \(B' = (-(-9), 5) = (9, 5)\)

3. For point \(C(2, -7)\):
- \(C' = (-(-7), 2) = (7, 2)\)

So, the coordinates of the points after rotating them 90 degrees counterclockwise about the origin are:

- \(A'(1, 5)\)
- \(B'(9, 5)\)
- \(C'(7, 2)\)

Thus, the new coordinates are:
- \(A' = (1, 5)\)
- \(B' = (9, 5)\)
- \(C' = (7, 2)\)