Question
Parallelogram JKLM and the image of JKLM are graphed on the coordinate grid below.
On a coordinate plane, parallelogram J K L M has points (negative 2, 0), (negative 2, negative 3), (negative 4, negative 2), (negative 4, 1). Parallelogram J prime K prime L prime M prime has points (2, 0), (2, 3), (4, 2), (4, negative 1).
Which statements describe the rotation about the origin that transformed JKLM to J’K’L’M’? Select 3 options.
counterclockwise rotation
clockwise rotation
90° rotation
45° rotation
180° rotation
On a coordinate plane, parallelogram J K L M has points (negative 2, 0), (negative 2, negative 3), (negative 4, negative 2), (negative 4, 1). Parallelogram J prime K prime L prime M prime has points (2, 0), (2, 3), (4, 2), (4, negative 1).
Which statements describe the rotation about the origin that transformed JKLM to J’K’L’M’? Select 3 options.
counterclockwise rotation
clockwise rotation
90° rotation
45° rotation
180° rotation
Answers
GPT-4o mini
To determine the rotation that transformed parallelogram JKLM to J'K'L'M', we need to analyze the coordinates of the points in both parallelograms.
- The points of JKLM are:
- J(-2, 0)
- K(-2, -3)
- L(-4, -2)
- M(-4, 1)
- The points of J'K'L'M' are:
- J'(2, 0)
- K'(2, 3)
- L'(4, 2)
- M'(4, -1)
To identify the transformation, let's look at the transformations applied to each coordinate, particularly focusing on the x and y values:
1. **For J (-2, 0) to J' (2, 0)**:
- The x-coordinate changes from -2 to 2, which is equivalent to a transformation from (-x, y).
2. **For K (-2, -3) to K' (2, 3)**:
- The x-coordinate changes from -2 to 2 (same as J), and the y-coordinate changes from -3 to 3, which suggests that for K, we again have (x, y) transformed to (-x, -y).
3. **For L (-4, -2) to L' (4, 2)**:
- Again, the x-coordinate from -4 to 4 indicates a reflection over the y-axis, and the y-coordinate from -2 to 2 indicates a reflection over the x-axis.
4. **For M (-4, 1) to M' (4, -1)**:
- Consistent with the others, we see a change from -4 to 4 in the x-coordinate, and 1 to -1 in the y-coordinate.
From these points, it appears that each point follows a pattern that suggests a 180° rotation about the origin, since both the x and y coordinates flip their signs.
### Summary:
The correct transformations can thus be summarized to:
1. **180° rotation**
2. **Counterclockwise rotation** (180° counterclockwise is the same as 180° clockwise, but we often denote 180° as counterclockwise)
3. **Clockwise rotation** (for the same reason as above, a 180° implies both)
### Final Selections:
So the three statements that describe the rotation about the origin that transformed JKLM to J’K’L’M’ are:
- 180° rotation
- Counterclockwise rotation
- Clockwise rotation
- The points of JKLM are:
- J(-2, 0)
- K(-2, -3)
- L(-4, -2)
- M(-4, 1)
- The points of J'K'L'M' are:
- J'(2, 0)
- K'(2, 3)
- L'(4, 2)
- M'(4, -1)
To identify the transformation, let's look at the transformations applied to each coordinate, particularly focusing on the x and y values:
1. **For J (-2, 0) to J' (2, 0)**:
- The x-coordinate changes from -2 to 2, which is equivalent to a transformation from (-x, y).
2. **For K (-2, -3) to K' (2, 3)**:
- The x-coordinate changes from -2 to 2 (same as J), and the y-coordinate changes from -3 to 3, which suggests that for K, we again have (x, y) transformed to (-x, -y).
3. **For L (-4, -2) to L' (4, 2)**:
- Again, the x-coordinate from -4 to 4 indicates a reflection over the y-axis, and the y-coordinate from -2 to 2 indicates a reflection over the x-axis.
4. **For M (-4, 1) to M' (4, -1)**:
- Consistent with the others, we see a change from -4 to 4 in the x-coordinate, and 1 to -1 in the y-coordinate.
From these points, it appears that each point follows a pattern that suggests a 180° rotation about the origin, since both the x and y coordinates flip their signs.
### Summary:
The correct transformations can thus be summarized to:
1. **180° rotation**
2. **Counterclockwise rotation** (180° counterclockwise is the same as 180° clockwise, but we often denote 180° as counterclockwise)
3. **Clockwise rotation** (for the same reason as above, a 180° implies both)
### Final Selections:
So the three statements that describe the rotation about the origin that transformed JKLM to J’K’L’M’ are:
- 180° rotation
- Counterclockwise rotation
- Clockwise rotation