Question

In the triangle shown in your image:

If we apply a 90-degree clockwise rotation around the origin, each point's coordinates will transform from (x, y) to (y, -x). Let’s calculate this for the points A, B, and C:

Point A (-8, 2) becomes Point A’ (2, 8).

Point B (-8, 8) becomes Point B’ (8, 8).

Point C (-5, 2) becomes Point C’ (2, 5).

Now, the new triangle (A’, B’, C’) will be positioned differently on the coordinate plane. The shape and size remain the same—it’s like the triangle turned as if on a pivot.
Use rotation mapping to locate C′
after a −90
-degree (clockwise) rotation about the origin.

(1 point)
C′
(
,
)

Answer 1

To apply a \(-90\)-degree (clockwise) rotation about the origin, we use the transformation rule \((x, y) \to (-y, x)\).

Given Point C \((-5, 2)\), we can find the new coordinates \(C'\) as follows:

1. Identify the coordinates of Point C:
\[
C(-5, 2)
\]

2. Apply the transformation:
\[
C' = (-y, x) = (-2, -5)
\]

Thus, the new coordinates of \(C'\) after a \(-90\)-degree clockwise rotation about the origin are:

\[
C' = (-2, -5)
\]

So the answer is:

\(C'(-2, -5)\)