Question

Triangle DEF has coordinates D(4,−1), E(5, 2), and F(1, 2). Determine the coordinates of the vertices of the image after a rotation 180° about the origin.

A) D'(5,−1), E'(6, 2), and F'(2, 2)

B) D'(1, 0), E'(2, 3), and F'(−2, 3)

C) D'(−4, 1), E'(−5,−2), and F'(−1,−2)

D) D'(−1,−4), E'(2,−5),
and F'(2,−1)

Answer 1

Explanation:

To determine the coordinates of the vertices of the image after a rotation of 180 degrees about the origin, we need to apply the following transformation to each vertex:

(x', y') = (-x, -y)

Here are the steps to find the new coordinates of each vertex:

Vertex D(4, -1):

x' = -4
y' = -(-1) = 1

Therefore, the new coordinates of vertex D are D'(-4, 1).

Vertex E(5, 2):

x' = -5
y' = -2

Therefore, the new coordinates of vertex E are E'(-5, -2).

Vertex F(1, 2):

x' = -1
y' = -2

Therefore, the new coordinates of vertex F are F'(-1, -2).

Therefore, the correct answer is option C) D'(-4, 1), E'(-5, -2), and F'(-1, -2).