Question

Triangle XYZ is rotated 90° counterclockwise about the origin.

On a coordinate plane, triangle X Y Z has points (1, 3), (4, negative 1), (1, negative 1).

What are the coordinates of point Y’?
(4, –2)
(1, 4)
(–4, 1)
(–1, –4)

Answer 1

To rotate a point \((x, y)\) 90° counterclockwise about the origin, the new coordinates \((x', y')\) can be determined using the formula:

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

For point \(Y\) with coordinates \((4, -1)\):

1. Identify \(x\) and \(y\):
- \(x = 4\)
- \(y = -1\)

2. Apply the 90° rotation formula:
\[
x' = -(-1) = 1
\]
\[
y' = 4
\]

Thus, the new coordinates of point \(Y'\) after the rotation are \((1, 4)\).

So, the correct answer is:
**(1, 4)**.