Question

Use△BCD in the figure shown.

What are the vertices of the image r(90°, O) (△BCD)?

The graph with X-coordinate marks -3, 0, 3 and Y-coordinate mark -3, 0, 3. The triangle BCD with coordinates B at (-3, 3), C at (4, 1), D at (0, -2).

A. B'(−3, −3), C'(−1, 4), D'(2, 0)
B. B'(3, 3), C'(1, −4), D'(−2, 0)
C. B'(3, −3), C'(1, 4), D'(0, 2)
D. B'(−3, −3), C'(−1, −4), D'(0, −2)

Answer 1

To determine the vertices of the image of triangle BCD after a rotation of 90° counterclockwise around the origin (O), we can use the rotation formula.

The rotation of a point \((x, y)\) by 90° counterclockwise around the origin can be computed using:
\[
(x', y') = (-y, x)
\]

Now, let's apply this formula to each vertex of triangle BCD:

1. **Point B(-3, 3)**:
\[
B' = (-3, 3) \rightarrow B' = (-3, -(-3)) = (-3, -3)
\]

2. **Point C(4, 1)**:
\[
C' = (4, 1) \rightarrow C' = (-1, 4)
\]

3. **Point D(0, -2)**:
\[
D' = (0, -2) \rightarrow D' = (-(-2), 0) = (2, 0)
\]

Therefore, the coordinates of the vertices of the image \(r(90°, O)(\triangle BCD)\) are:
\[
B'(-3, -3), C'(-1, 4), D'(2, 0)
\]

Thus, the correct answer is:
**A. B'(-3, -3), C'(-1, 4), D'(2, 0)**.