Question

Rotate △ABC 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?

Answer 1

To rotate a point \((x, y)\) counterclockwise by 90 degrees about the origin, the new coordinates \((x', y')\) can be calculated using the formula:

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

Let's apply this to each vertex of triangle \( △ABC \):

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

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

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

Thus, the coordinates of the rotated triangle \( △A′B′C′ \) are:
- \( A' (1, 5) \)
- \( B' (9, 5) \)
- \( C' (7, 2) \)