Question
Match up the key terms with their definition.(8 points)
image
transformation
line of symmetry
rotation
function
origin
rigid motion
reflection
a change in size, position, or orientation of a geometric shape
the transformation of a shape across a line of reflection
a rigid transformation resulting in a mirror image
the production of an image by or as if by using a mirror
an imaginary line midway between each point of a preimage and its corresponding point o the image after a feflection
the intersection of coordinate axes
a transformation that preserves distance and angle measure; also known as a rigid tansformation
the circular motion o a figure around a fixer center point
a special relationship between terms in an eqution where each input has a single output; many times it is written as f(x), where x is a value that is inputted
the new position of a point, line, or figure after a transformation
Drag and drop the words into the correct locations. Answers may be used more that once.(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A child on a swing. Response area
A child going down a slide. Response area
An apple failing from a tree.Response area
A baseball bat being swung.Response area
A child doing a cartwheel.Response area
answers is a translation
is not a translation
If coordinates (-4,7) undergo a translation vector of <-4,8> in the coordinate plane, what would the resulting coordinated be?(1 point)
Responses
(-8,-1)
(-8,-1)
(-8,15)
(-8,15)
(-8,-1)
(-8,-1)
(0,-1)
Raiph draws a triangle on the coordinate grid. Its vertices are at (7,-3), (4, -7), and (-1,5). He translates this triangle, 4 units up and 2 units to the left. What are the coordinates of the lowest vertex on the translated triangle?(1 point)
Responses
(2,-3)
(2,-3)
(2,-11)
(2,-11)
(6,-3)
(6,-3)
(2,6)
A point is translated on the coordinate plane from (4,-8) to (4,-6). Create a function to show this translation. Which function shows the appropriate translation?(1 point)
Responses
g(y)= y+ 2
g(y)= y+ 2
f(x)= x+ 2
f(x)= x+ 2
g(y)= y- 2
g(y)= y- 2
g(y)= y
Apply geometric motions to reflect figures. Brianna reflects point P over a line of reflection, resulting in point P'. If points P and P' have the same y coordinate, what must be true?(1 point)
Responses
The line of reflection is the y-axis.
The line of reflection is the y-axis.
The line of reflection is the x-axis.
The line of reflection is the x-axis.
The line of reflection is vertical.
The line of reflection is vertical.
The line of reflection is horizontal.
Question
The function f(x)=(x + 1)2
is reflected over the y-axis to create g(x). Identify the equation for g(x).(1 point)
Responses
g(x) = - (x + 1)2
g(x) = - (x + 1)2
g(x) = (-x + 1)2
g(x) = (-x + 1)2
g(x) = -x2
+1
g(x) = -x2+1
g(x) = (-x - 1)2
Which of the following mapping is used for a 270 degree (counterclockwise) rotation?(1 point)
Responses
(x, y)→(y, −x)
(x, y)→(y, −x)
(x, y)→(−y, x)
(x, y)→(−y, x)
(x, y)→(−y, −x)
(x, y)→(−y, −x)
(x, y)→(−x, −y)
The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?(1 point)
Responses
a 270 degrees counterclockwise rotation
a 270 degrees counterclockwise rotation
a reflection over the line y = x
a reflection over the line y = x
a translation
a translation
a dilation with a scale factor of 1/4
image
transformation
line of symmetry
rotation
function
origin
rigid motion
reflection
a change in size, position, or orientation of a geometric shape
the transformation of a shape across a line of reflection
a rigid transformation resulting in a mirror image
the production of an image by or as if by using a mirror
an imaginary line midway between each point of a preimage and its corresponding point o the image after a feflection
the intersection of coordinate axes
a transformation that preserves distance and angle measure; also known as a rigid tansformation
the circular motion o a figure around a fixer center point
a special relationship between terms in an eqution where each input has a single output; many times it is written as f(x), where x is a value that is inputted
the new position of a point, line, or figure after a transformation
Drag and drop the words into the correct locations. Answers may be used more that once.(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A child on a swing. Response area
A child going down a slide. Response area
An apple failing from a tree.Response area
A baseball bat being swung.Response area
A child doing a cartwheel.Response area
answers is a translation
is not a translation
If coordinates (-4,7) undergo a translation vector of <-4,8> in the coordinate plane, what would the resulting coordinated be?(1 point)
Responses
(-8,-1)
(-8,-1)
(-8,15)
(-8,15)
(-8,-1)
(-8,-1)
(0,-1)
Raiph draws a triangle on the coordinate grid. Its vertices are at (7,-3), (4, -7), and (-1,5). He translates this triangle, 4 units up and 2 units to the left. What are the coordinates of the lowest vertex on the translated triangle?(1 point)
Responses
(2,-3)
(2,-3)
(2,-11)
(2,-11)
(6,-3)
(6,-3)
(2,6)
A point is translated on the coordinate plane from (4,-8) to (4,-6). Create a function to show this translation. Which function shows the appropriate translation?(1 point)
Responses
g(y)= y+ 2
g(y)= y+ 2
f(x)= x+ 2
f(x)= x+ 2
g(y)= y- 2
g(y)= y- 2
g(y)= y
Apply geometric motions to reflect figures. Brianna reflects point P over a line of reflection, resulting in point P'. If points P and P' have the same y coordinate, what must be true?(1 point)
Responses
The line of reflection is the y-axis.
The line of reflection is the y-axis.
The line of reflection is the x-axis.
The line of reflection is the x-axis.
The line of reflection is vertical.
The line of reflection is vertical.
The line of reflection is horizontal.
Question
The function f(x)=(x + 1)2
is reflected over the y-axis to create g(x). Identify the equation for g(x).(1 point)
Responses
g(x) = - (x + 1)2
g(x) = - (x + 1)2
g(x) = (-x + 1)2
g(x) = (-x + 1)2
g(x) = -x2
+1
g(x) = -x2+1
g(x) = (-x - 1)2
Which of the following mapping is used for a 270 degree (counterclockwise) rotation?(1 point)
Responses
(x, y)→(y, −x)
(x, y)→(y, −x)
(x, y)→(−y, x)
(x, y)→(−y, x)
(x, y)→(−y, −x)
(x, y)→(−y, −x)
(x, y)→(−x, −y)
The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?(1 point)
Responses
a 270 degrees counterclockwise rotation
a 270 degrees counterclockwise rotation
a reflection over the line y = x
a reflection over the line y = x
a translation
a translation
a dilation with a scale factor of 1/4
Answers
Answered by
GPT-4o mini
Here are the answers to your queries, organized accordingly:
**Match up the key terms with their definitions:**
1. **image** - the new position of a point, line, or figure after a transformation
2. **transformation** - a change in size, position, or orientation of a geometric shape
3. **line of symmetry** - an imaginary line midway between each point of a preimage and its corresponding point of the image after a reflection
4. **rotation** - the circular motion of a figure around a fixed center point
5. **function** - a special relationship between terms in an equation where each input has a single output; many times it is written as f(x), where x is a value that is inputted
6. **origin** - the intersection of coordinate axes
7. **rigid motion** - a transformation that preserves distance and angle measure; also known as a rigid transformation
8. **reflection** - a rigid transformation resulting in a mirror image
---
**Drag and drop the words into the correct locations:**
- **A child on a swing.** is not a translation
- **A child going down a slide.** is not a translation
- **An apple falling from a tree.** is a translation
- **A baseball bat being swung.** is not a translation
- **A child doing a cartwheel.** is not a translation
---
**If coordinates (-4,7) undergo a translation vector of <-4,8>, what would the resulting coordinates be?**
- The resulting coordinates would be: **(-8,15)**
---
**Raiph draws a triangle on the coordinate grid. Its vertices are at (7,-3), (4, -7), and (-1,5). He translates this triangle, 4 units up and 2 units to the left. What are the coordinates of the lowest vertex on the translated triangle?**
- The coordinates of the lowest vertex after the translation would be: **(2,-11)**
---
**A point is translated on the coordinate plane from (4,-8) to (4,-6). Create a function to show this translation. Which function shows the appropriate translation?**
- The function that shows the appropriate translation is: **g(y) = y + 2**
---
**Apply geometric motions to reflect figures. Brianna reflects point P over a line of reflection, resulting in point P'. If points P and P' have the same y coordinate, what must be true?**
- The correct response is: **The line of reflection is horizontal.**
---
**The function f(x)=(x + 1)^2 is reflected over the y-axis to create g(x). Identify the equation for g(x).**
- The equation for g(x) after reflection would be: **g(x) = (-x + 1)^2**
---
**Which of the following mappings is used for a 270-degree (counterclockwise) rotation?**
- The mapping used for a 270-degree (counterclockwise) rotation is: **(x, y) → (y, −x)**
---
**The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?**
- This is equivalent to: **a 270 degrees counterclockwise rotation.**
**Match up the key terms with their definitions:**
1. **image** - the new position of a point, line, or figure after a transformation
2. **transformation** - a change in size, position, or orientation of a geometric shape
3. **line of symmetry** - an imaginary line midway between each point of a preimage and its corresponding point of the image after a reflection
4. **rotation** - the circular motion of a figure around a fixed center point
5. **function** - a special relationship between terms in an equation where each input has a single output; many times it is written as f(x), where x is a value that is inputted
6. **origin** - the intersection of coordinate axes
7. **rigid motion** - a transformation that preserves distance and angle measure; also known as a rigid transformation
8. **reflection** - a rigid transformation resulting in a mirror image
---
**Drag and drop the words into the correct locations:**
- **A child on a swing.** is not a translation
- **A child going down a slide.** is not a translation
- **An apple falling from a tree.** is a translation
- **A baseball bat being swung.** is not a translation
- **A child doing a cartwheel.** is not a translation
---
**If coordinates (-4,7) undergo a translation vector of <-4,8>, what would the resulting coordinates be?**
- The resulting coordinates would be: **(-8,15)**
---
**Raiph draws a triangle on the coordinate grid. Its vertices are at (7,-3), (4, -7), and (-1,5). He translates this triangle, 4 units up and 2 units to the left. What are the coordinates of the lowest vertex on the translated triangle?**
- The coordinates of the lowest vertex after the translation would be: **(2,-11)**
---
**A point is translated on the coordinate plane from (4,-8) to (4,-6). Create a function to show this translation. Which function shows the appropriate translation?**
- The function that shows the appropriate translation is: **g(y) = y + 2**
---
**Apply geometric motions to reflect figures. Brianna reflects point P over a line of reflection, resulting in point P'. If points P and P' have the same y coordinate, what must be true?**
- The correct response is: **The line of reflection is horizontal.**
---
**The function f(x)=(x + 1)^2 is reflected over the y-axis to create g(x). Identify the equation for g(x).**
- The equation for g(x) after reflection would be: **g(x) = (-x + 1)^2**
---
**Which of the following mappings is used for a 270-degree (counterclockwise) rotation?**
- The mapping used for a 270-degree (counterclockwise) rotation is: **(x, y) → (y, −x)**
---
**The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?**
- This is equivalent to: **a 270 degrees counterclockwise rotation.**