Question

graph the image of △cde after a rotation 180° clockwise around the origin.

Explanation:

Step1: Find coordinates of C, D, E

From the graph:

• \( D(-7, 0) \)
• \( C(-7, -8) \)
• \( E(-4, -9) \)

Step2: Apply 180° rotation rule

The rule for a \( 180^\circ \) clockwise (or counterclockwise) rotation around the origin is \( (x, y) \to (-x, -y) \).

• For \( D(-7, 0) \):

\( (-(-7), -0) = (7, 0) \)

• For \( C(-7, -8) \):

\( (-(-7), -(-8)) = (7, 8) \)

• For \( E(-4, -9) \):

\( (-(-4), -(-9)) = (4, 9) \)

Step3: Plot the new points

Plot \( D'(7, 0) \), \( C'(7, 8) \), and \( E'(4, 9) \), then connect them to form the rotated triangle.

Answer:

The image of \( \triangle CDE \) after a \( 180^\circ \) clockwise rotation around the origin has vertices at \( D'(7, 0) \), \( C'(7, 8) \), and \( E'(4, 9) \). (Graph by plotting these points and connecting them.)