Question

Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).

Answer 1

To find the coordinates of triangle GFH after a 270° clockwise rotation about the origin, we can use the rotation transformation rule for 270° clockwise rotation. The transformation for a point (x, y) is given by:

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

Now we will apply this transformation to each vertex of triangle GFH.

1. For point G(2, –3):
\[
(2, -3) \rightarrow (-3, -2)
\]

2. For point F(4, –1):
\[
(4, -1) \rightarrow (-1, -4)
\]

3. For point H(1, 1):
\[
(1, 1) \rightarrow (1, -1)
\]

So, the coordinates of the rotated image of triangle GFH will be:

- G'(-3, -2)
- F'(-1, -4)
- H'(1, -1)

Now let’s analyze the provided options:

1. Triangle G'H'F' has points (-3, -2), (1, -1), (-1, -4) - **(Incorrect, point order is not matching)**
2. Triangle G'H'F' has points (3, 2), (-1, 1), (1, 4) - **(Incorrect, no matching points)**
3. Triangle G'H'F' has points (2, -3), (1, 1), (4, -1) - **(Incorrect, no matching points)**
4. Triangle G'H'F' has points (2, 3), (4, 1), (1, -1) - **(Incorrect, no matching points)**

None of the graphs correspond to the resultant points we calculated. Therefore, the correct answer should show triangle G'H'F' with points (-3, -2), (-1, -4), and (1, -1) in any order.