Question
Transformations unit test ninth grade
Answers
GPT-4o mini
Creating a unit test on transformations for a ninth-grade math class can be an effective way to evaluate students' understanding of geometric transformations, including translations, rotations, reflections, and dilations. Below is a sample unit test that consists of a variety of question types (multiple choice, short answer, and problem-solving).
### Transformations Unit Test
**Name: _______________________**
**Date: ________________________**
#### Multiple Choice (2 points each)
1. Which of the following describes a translation?
a) A shape is flipped over a line.
b) A shape is rotated around a point.
c) A shape is moved to a different location without changing its size or orientation.
d) A shape is resized while keeping the same proportions.
2. If triangle ABC has vertices A(1, 2), B(3, 4), and C(2, 5), what are the coordinates of triangle ABC after a reflection over the y-axis?
a) A(-1, 2), B(-3, 4), C(-2, 5)
b) A(1, -2), B(3, -4), C(2, -5)
c) A(-1, 2), B(-3, -4), C(-2, -5)
d) A(-1, -2), B(-3, -4), C(-2, -5)
3. A shape is dilated by a scale factor of 2. What happens to the area of the shape?
a) The area remains the same.
b) The area doubles.
c) The area is quadrupled.
d) The area is halved.
4. Which transformation would change the orientation of a shape?
a) Translation
b) Dilation
c) Reflection
d) All of the above
#### Short Answer (3 points each)
5. Describe the transformation that occurs when a rectangle with vertices (2, 3), (2, 6), (5, 3), and (5, 6) is reflected over the line y = x. Provide the coordinates of the new vertices.
6. Given triangle PQR with vertices P(2, -1), Q(4, 3), R(1, 4), apply a 90-degree clockwise rotation around the origin and list the coordinates of the new vertices.
#### Problem Solving (5 points each)
7. A square has vertices at A(1, 1), B(1, 4), C(4, 1), and D(4, 4). Describe and perform the following transformations in order:
a) Reflect the square over the x-axis.
b) Translate the new shape 3 units to the right and 2 units up.
c) Determine the area of the final shape.
8. An equilateral triangle has a side length of 6 units. If it is dilated by a scale factor of ½, what is the side length of the new triangle? Show your work.
#### Total Points: ________ / 40
### Answer Key (for teachers)
#### Multiple Choice
1. c
2. a
3. c
4. c
#### Short Answer
5. Reflecting over line y = x:
- A(2, 3) -> A'(3, 2)
- B(2, 6) -> B'(6, 2)
- C(5, 3) -> C'(3, 5)
- D(5, 6) -> D'(6, 5)
New vertices: (3, 2), (6, 2), (3, 5), (6, 5)
6. 90-degree clockwise rotation:
- P(2, -1) -> P'(-1, -2)
- Q(4, 3) -> Q'(-3, 4)
- R(1, 4) -> R'(-4, 1)
New vertices: (-1, -2), (-3, 4), (-4, 1)
#### Problem Solving
7.
- Reflecting over the x-axis gives:
- A(1, 1) -> A(1, -1)
- B(1, 4) -> B(1, -4)
- C(4, 1) -> C(4, -1)
- D(4, 4) -> D(4, -4)
- Translating 3 units right and 2 units up gives:
- A(1, -1) -> A(4, 1)
- B(1, -4) -> B(4, -2)
- C(4, -1) -> C(7, 1)
- D(4, -4) -> D(7, -2)
- Area of the square remains 9 square units.
8. The new side length is 6 * 1/2 = 3 units.
Feel free to modify questions and point values as needed to fit your specific curriculum and classroom requirements!
### Transformations Unit Test
**Name: _______________________**
**Date: ________________________**
#### Multiple Choice (2 points each)
1. Which of the following describes a translation?
a) A shape is flipped over a line.
b) A shape is rotated around a point.
c) A shape is moved to a different location without changing its size or orientation.
d) A shape is resized while keeping the same proportions.
2. If triangle ABC has vertices A(1, 2), B(3, 4), and C(2, 5), what are the coordinates of triangle ABC after a reflection over the y-axis?
a) A(-1, 2), B(-3, 4), C(-2, 5)
b) A(1, -2), B(3, -4), C(2, -5)
c) A(-1, 2), B(-3, -4), C(-2, -5)
d) A(-1, -2), B(-3, -4), C(-2, -5)
3. A shape is dilated by a scale factor of 2. What happens to the area of the shape?
a) The area remains the same.
b) The area doubles.
c) The area is quadrupled.
d) The area is halved.
4. Which transformation would change the orientation of a shape?
a) Translation
b) Dilation
c) Reflection
d) All of the above
#### Short Answer (3 points each)
5. Describe the transformation that occurs when a rectangle with vertices (2, 3), (2, 6), (5, 3), and (5, 6) is reflected over the line y = x. Provide the coordinates of the new vertices.
6. Given triangle PQR with vertices P(2, -1), Q(4, 3), R(1, 4), apply a 90-degree clockwise rotation around the origin and list the coordinates of the new vertices.
#### Problem Solving (5 points each)
7. A square has vertices at A(1, 1), B(1, 4), C(4, 1), and D(4, 4). Describe and perform the following transformations in order:
a) Reflect the square over the x-axis.
b) Translate the new shape 3 units to the right and 2 units up.
c) Determine the area of the final shape.
8. An equilateral triangle has a side length of 6 units. If it is dilated by a scale factor of ½, what is the side length of the new triangle? Show your work.
#### Total Points: ________ / 40
### Answer Key (for teachers)
#### Multiple Choice
1. c
2. a
3. c
4. c
#### Short Answer
5. Reflecting over line y = x:
- A(2, 3) -> A'(3, 2)
- B(2, 6) -> B'(6, 2)
- C(5, 3) -> C'(3, 5)
- D(5, 6) -> D'(6, 5)
New vertices: (3, 2), (6, 2), (3, 5), (6, 5)
6. 90-degree clockwise rotation:
- P(2, -1) -> P'(-1, -2)
- Q(4, 3) -> Q'(-3, 4)
- R(1, 4) -> R'(-4, 1)
New vertices: (-1, -2), (-3, 4), (-4, 1)
#### Problem Solving
7.
- Reflecting over the x-axis gives:
- A(1, 1) -> A(1, -1)
- B(1, 4) -> B(1, -4)
- C(4, 1) -> C(4, -1)
- D(4, 4) -> D(4, -4)
- Translating 3 units right and 2 units up gives:
- A(1, -1) -> A(4, 1)
- B(1, -4) -> B(4, -2)
- C(4, -1) -> C(7, 1)
- D(4, -4) -> D(7, -2)
- Area of the square remains 9 square units.
8. The new side length is 6 * 1/2 = 3 units.
Feel free to modify questions and point values as needed to fit your specific curriculum and classroom requirements!