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).

Answer 1

To find the coordinates of the points of triangle PQR after a 90° counterclockwise rotation around the origin, we can use the rule for rotation:

When a point (x, y) is rotated 90° counterclockwise, its new coordinates become (-y, x).

Let’s apply this to each vertex of triangle PQR.

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 rotation, the new coordinates of the triangle P’Q’R’ are:
- P’ = (1, -3)
- Q’ = (3, -3)
- R’ = (2, -6)

Now we check the options given in the problem to find which one matches the coordinates (1, -3), (3, -3), (2, -6):

- The first option has points (–3, –1), (–3, –3), (–6, –2).
- The second option has points (–1, 3), (–3, 3), (–2, 6).
- The third option has points (1, –3), (3, –3), (2, –6).
- The fourth option has points (3, –1), (3, –3), (6, –2).

The third option matches the coordinates we calculated, so the correct graph representing triangle P’Q’R’ after the rotation is:

**Triangle P'Q'R' has points (1, -3), (3, -3), (2, -6).**