A triangle has vertices W (-4,7), Q (-1,-1) and Z (-7,-2). Apply rotation mapping rules to find the coordinates of W' after a 90-degree rotation about the origin. (1 point)

Answer 1

To rotate a point \((x, y)\) by 90 degrees counterclockwise about the origin, the new coordinates \((x', y')\) can be found using the following transformation rules:

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

Now, let's apply this to the point \(W (-4, 7)\).

1. Identify the coordinates of W:

   • \(x = -4\)
   • \(y = 7\)

2. Apply the rotation rules:

   • For \(W'\), the new coordinates will be: \[ x' = -y = -7 \] \[ y' = x = -4 \]

3. Combine the results:

   • The coordinates of \(W'\) after the rotation are: \[ W' = (-7, -4) \]

Thus, the coordinates of \(W'\) after a 90-degree rotation about the origin are \(\boxed{(-7, -4)}\).