Question

parallelogram abcd is rotated 180° clockwise about the origin to produce abcd. write the coordinates of each vertex in the image. a(( ), ( )) b(( ), ( )) c(( ), ( )) d(( ), ( ))

Explanation:

Step1: Find original coordinates

From the graph, we can see the coordinates of the original vertices:

• \( A(5, 3) \)
• \( B(5, 4) \)
• \( C(10, 8) \)
• \( D(10, 7) \)

Step2: Apply 180° rotation rule

The rule for rotating a point \( (x, y) \) 180° clockwise (or counterclockwise) about the origin is \( (x, y) \to (-x, -y) \).

For \( A(5, 3) \):

Applying the rule, \( A'(-5, -3) \)

For \( B(5, 4) \):

Applying the rule, \( B'(-5, -4) \)

For \( C(10, 8) \):

Applying the rule, \( C'(-10, -8) \)

For \( D(10, 7) \):

Applying the rule, \( D'(-10, -7) \)

Answer:

\( A'(-5, -3) \)
\( B'(-5, -4) \)
\( C'(-10, -8) \)
\( D'(-10, -7) \)