Question
Parallelogram JKLM is shown on the coordinate plane below:
Parallelogram JKLM with ordered pairs at J negative 6, 2, at K negative 4, 6, at L negative 3, 3, at M negative 5, negative 1.
If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side JM in the image parallelogram?
J′(−2, −6); M′(1, −5)
J′(6, 2); M′(−5, 1)
J′(2, 6); M′(−1, 5)
J′(6, −2); M′(5, 1)
Answers
GPT-4o mini
To find the coordinates of the endpoints of the side congruent to side JM in parallelogram JKLM after a 270° clockwise rotation around the origin, we first need to determine the coordinates of points J and M, then apply the rotation transformation.
The coordinates for points J and M are:
- J(-6, 2)
- M(-5, -1)
A 270° clockwise rotation around the origin can be performed by using the transformation:
\[
(x, y) \rightarrow (y, -x)
\]
Let's apply this transformation to points J and M.
1. **Rotate point J(-6, 2)**:
\[
J' = (2, -(-6)) = (2, 6)
\]
2. **Rotate point M(-5, -1)**:
\[
M' = (-1, -(-5)) = (-1, 5)
\]
So after the 270° clockwise rotation, we have:
- J' = (2, 6)
- M' = (-1, 5)
Looking at the provided options for coordinates of J' and M', we find:
- **J'(2, 6); M'(-1, 5)**
Thus, the correct answer is:
**J′(2, 6); M′(−1, 5)**.
The coordinates for points J and M are:
- J(-6, 2)
- M(-5, -1)
A 270° clockwise rotation around the origin can be performed by using the transformation:
\[
(x, y) \rightarrow (y, -x)
\]
Let's apply this transformation to points J and M.
1. **Rotate point J(-6, 2)**:
\[
J' = (2, -(-6)) = (2, 6)
\]
2. **Rotate point M(-5, -1)**:
\[
M' = (-1, -(-5)) = (-1, 5)
\]
So after the 270° clockwise rotation, we have:
- J' = (2, 6)
- M' = (-1, 5)
Looking at the provided options for coordinates of J' and M', we find:
- **J'(2, 6); M'(-1, 5)**
Thus, the correct answer is:
**J′(2, 6); M′(−1, 5)**.