On a coordinate plane, a triangle has points A (negative 5, 3), B (negative 2, 4), C (negative 2, 2).

Question

Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?

(4, 2)
(2, 4)
(–4, –2)
(–2, –4)

Answer 1

To rotate a point \((x, y)\) about the origin by 270° (which is equivalent to a 90° clockwise rotation), you can use the following transformation:

\[ (x, y) \rightarrow (y, -x) \]

We need to apply this transformation to point B which has coordinates \((-2, 4)\).

Applying the transformation:

\[ (-2, 4) \rightarrow (4, -(-2)) = (4, 2) \]

Therefore, the coordinates of the image of point B after the triangle is rotated 270° about the origin are \((4, 2)\).

The correct answer is: \((4, 2)\)