To determine the coordinates of [tex]\(C'\)[/tex] after rotating point [tex]\(C(1,2)\)[/tex] by [tex]\(90^\circ\)[/tex] clockwise, follow these steps:
1. Understand Rotation Transformation:
The formula for rotating a point [tex]\((x, y)\)[/tex] by [tex]\(90^\circ\)[/tex] clockwise around the origin is:
[tex]\[
(x, y) \rightarrow (y, -x)
\][/tex]
2. Apply the Rotation Formula:
- Identify the coordinates of point [tex]\(C\)[/tex], which are [tex]\((1, 2)\)[/tex].
- Substitute [tex]\(x = 1\)[/tex] and [tex]\(y = 2\)[/tex] into the rotation formula:
[tex]\[
(x, y) \rightarrow (y, -x) \rightarrow (2, -1)
\][/tex]
3. Determine the New Coordinates:
- After rotating [tex]\(C\)[/tex] by [tex]\(90^\circ\)[/tex] clockwise, the new coordinates [tex]\(C'\)[/tex] are:
[tex]\[
C' = (2, -1)
\][/tex]
Thus, the ordered pair of [tex]\(C'\)[/tex] after rotating point [tex]\(C(1,2)\)[/tex] by [tex]\(90^\circ\)[/tex] clockwise is:
[tex]\[ C^{\prime}(2, -1) \][/tex]
