What are the new coordinates for vertex B after rotating the triangle with vertices A (2, 3), B (-1, 2), and C (1, -3) counter-clockwise 90 degrees about the origin?

To find the new coordinates of vertex B after a 90-degree counter-clockwise rotation about the origin, we can use the formula that describes how points (x, y) transform under such a rotation. The transformation for a 90-degree counter-clockwise rotation can be represented as:

[

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

]

Applying this transformation to the coordinates of vertex B, which are initially (-1, 2):

1. Substitute -1 for x and 2 for y:

• The new x-coordinate becomes -y, which is -2.

• The new y-coordinate becomes x, which is -1.

Thus, the coordinates for vertex B after the rotation are (-2, -1). This means that the transformation has successfully shifted vertex B from its original position to the new position reflected in the answer choice.

The coordinates (-2, -1) represent the correct transformed position of vertex B after the specified rotation.