Question

transformations test (topic 4)
△abc is rotated 180 degrees clockwise about the origin to produce △abc. what are the coordinates of △abc?
image of coordinate grid with triangle abc
options:

• ( a(-2,1) ), ( b(-1,1) ), and ( c(1,-3) )
• ( a(2,-1) ), ( b(1,-1) ), and ( c(1,-3) )
• ( a(-1,-2) ), ( b(-1,-1) ), and ( c(-3,-1) )
• ( a(2,1) ), ( b(1,1) ), and ( c(1,3) )

Explanation:

Step1: Identify original coordinates

From the graph, find coordinates of \( A \), \( B \), \( C \).
\( A(-2, 1) \), \( B(-1, 1) \), \( C(-1, 3) \).

Step2: Apply 180° rotation rule

A 180° clockwise (or counterclockwise) rotation about the origin transforms a point \( (x, y) \) to \( (-x, -y) \).

• For \( A(-2, 1) \):

\( A' = (-(-2), -1) = (2, -1) \).

• For \( B(-1, 1) \):

\( B' = (-(-1), -1) = (1, -1) \).

• For \( C(-1, 3) \):

\( C' = (-(-1), -3) = (1, -3) \).

Answer:

\( A'(2, -1) \), \( B'(1, -1) \), and \( C'(1, -3) \) (the second option)