Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.

Question

A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1)

Answer 1

To find the image of point A(1, 5) after a 270° counterclockwise rotation, we can use the rotation transformation formulas. For a point \((x, y)\) that is rotated 270° counterclockwise around the origin, the transformations are given by:

\[ (x', y') = (y, -x) \]

So, we can apply this transformation to point A(1, 5):

1. Identify the coordinates:

   • \(x = 1\)
   • \(y = 5\)

2. Apply the transformation: \[ x' = y = 5 \] \[ y' = -x = -1 \]

Thus, the coordinates for A' after a 270° rotation counterclockwise are:

\[ A' = (5, -1) \]

Among the options provided, the correct answer is:

A′(5, −1).