Question

Use the graph to answer the question.

graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3

Determine the coordinates of polygon A′B′C′D' if polygon ABCD is rotated 180°.

A′(0, 0), B′(−2, 5), C′(5, 5), D'(3, 0)
A′(0, 0), B′(2, −5), C′(−5, −5), D'(−3, 0)
A′(0, 0), B′(−5, −2), C′(5, −5), D'(3, 0)
A′(0, 0), B′(−5, −2), C′(−5, 5), D'(0, 3)

Answer 1

Answer: the answer is (D) A′(0, 0), B′(−5, −2), C′(−5, 5), D'(0, 3).

Step-by-step explanation: To rotate the polygon 180°, we need to reflect each point over the line passing through the origin and perpendicular to the x-axis.

The point (0,0) will remain the same as it is the origin and the line of reflection passes through it.

To find the coordinates of B', we reflect the point (5,2) over the line to get (-5,-2), then we translate it 5 units to the left to get (-5+5, -2) = (-2, -5).

To find the coordinates of C', we reflect the point (5,-5) over the line to get (-5,5), then we translate it 5 units to the left to get (-5+5, 5) = (0, 5).

To find the coordinates of D', we reflect the point (0,-3) over the line to get (0,3).

Therefore, the coordinates of A', B', C', and D' are:

A' = (0,0)

B' = (-2,-5)

C' = (0,5)

D' = (0,3)

So the answer is (D) A′(0, 0), B′(−5, −2), C′(−5, 5), D'(0, 3).