Question

Rotate △A (5,-1) B (5,-9) C (2,-7)
90 degrees (counterclockwise) about the origin to create △A′B′C′
. What are the coordinates of the following points?(3 points)
A′
(
,
)

B′
(
,
)

C′
(
,
)

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 vertex of triangle \( \triangle ABC \).

1. **Point A (5, -1)**:
\[
A' = (-(-1), 5) = (1, 5)
\]

2. **Point B (5, -9)**:
\[
B' = (-(-9), 5) = (9, 5)
\]

3. **Point C (2, -7)**:
\[
C' = (-(-7), 2) = (7, 2)
\]

Thus, the coordinates of the points after the rotation are:
- \(A' (1, 5)\)
- \(B' (9, 5)\)
- \(C' (7, 2)\)

### Final coordinates:
- A′ (1, 5)
- B′ (9, 5)
- C′ (7, 2)