Question

What is the rotation of 180 degrees counterclockwise around the origin of the point (4, 2)?
A
(-2, 4)
B
(4, 2)
C
(2, -4)
D
(-4, -2)

Answer 1

To find the image of the point (4, 2) after a 180-degree counterclockwise rotation around the origin, you can use the following rule:

For a 180-degree rotation, the new coordinates \((x', y')\) of a point \((x, y)\) become:

\[
x' = -x
\]
\[
y' = -y
\]

So for the point (4, 2):

\[
x' = -4
\]
\[
y' = -2
\]

Thus, after the rotation, the new coordinates are \((-4, -2)\).

Therefore, the answer is:

**D (-4, -2)**.