Question

Triangle PQR has vertices P(–3, –1), Q(–3, –3), and R(–6, –2). The triangle is rotated 90° counterclockwise using the origin as the center of rotation. Which graph shows the image, triangle P’Q’R’?
On a coordinate plane, triangle P prime Q prime R prime has points (negative 3, negative 1), (negative 3, negative 3), (negative 6, negative 2).
On a coordinate plane, triangle P prime Q prime R prime has points (negative 1, 3), (negative 3, 3), (negative 2, 6).
On a coordinate plane, triangle P prime Q prime R prime has points (1, negative 3), (3, negative 3), (2, negative 6).
On a coordinate plane, triangle P prime Q prime R prime has points (3, negative 1), (3, negative 3), (6, negative 2). option 1 2 3 or 4

Answer 1

To rotate triangle PQR with vertices P(–3, –1), Q(–3, –3), and R(–6, –2) counterclockwise by 90 degrees around the origin, we can use the rotation transformation rules. Specifically, for a point (x, y), after a 90° counterclockwise rotation around the origin, the new coordinates become (–y, x).

Let's apply this to each vertex:

1. For point P(–3, –1):
- New coordinates: (–(–1), –3) = (1, –3)

2. For point Q(–3, –3):
- New coordinates: (–(–3), –3) = (3, –3)

3. For point R(–6, –2):
- New coordinates: (–(–2), –6) = (2, –6)

So, after the 90° counterclockwise rotation, the vertices of triangle P'Q'R' are P'(1, –3), Q'(3, –3), and R'(2, –6).

Now let's compare these with the options provided:

1. (–3, –1), (–3, –3), (–6, –2) - NOT the correct answer
2. (–1, 3), (–3, 3), (–2, 6) - NOT the correct answer
3. (1, –3), (3, –3), (2, –6) - THIS is the correct answer
4. (3, –1), (3, –3), (6, –2) - NOT the correct answer

So, the correct choice is option **3**.