Horizontal Dilations 2
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Question 1 of 4
1. Question
The points `A(-2,6)` and `B(8,0)` lie on `y=f(x)`. Find the coordinates of images `A` and `B` for `y=f(ax)` when `a=2`.
Correct
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A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilation (stretch/shrink) factor takes the form `y=f(ax)` where the horizontal dilation factor can be found with `\text(Factor) =1/a`.Alternatively, to find the image point coordinates, we take the
x-coordinate and multiply by the horizontal dilation factorMethod 1To find the image points for `A(-2,6)` and `B(8,0)` when `a=2` start by finding the horizontal dilation (stretch/shrink) factor `\text(Factor) =1/a`.`\text(Factor) =` `1/color(green)(2)` Simplify `\text(Factor) =` `1/2` Now multiply the `x`-coordinate in each point `A(-2,6)` and `B(8,0)` by the Factor (`1/2`).Point `A(-2,6)` becomes `(-2 xx 1/2,6)=(-1,6)`.Then, multiply the `x`-coordinate of `B(8,0)` by the Factor (`1/2`).Point `B(8,0)` becomes `(8 xx 1/2,0)=(4,0)`.Method 2To find the image points all you have to do is take the x-coordinates `A(x=-2)` and for `B(x=8)` and multiply each of them by the horizontal dilation factor of `1/2`For `A:(-2 xx 1/2, 6)=(-1,6)`For `B(8 xx 1/2,0)=(4,0)``A(-1,6)` and `B(4,0)` -
Question 2 of 4
2. Question
When `y=f(x)` is transformed to `y=f(ax)`, the coordinates become `(12,-3)`.
Find the original coordinates of `R` when `a=1/2`.Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilation (stretch/shrink) factor takes the form `y=f(ax)` where the horizontal dilation factor can be found with `\text(Factor) =1/a`.Alternatively, to find the original coordinates you can divide using `x/\text(Factor)`Method 1To find the original coordinates `(x,y)` when `a=1/2`. We start by finding the horizontal dilation (stretch/shrink) factor
`\text(Factor) =1/a`.`\text(Factor) =` `1/color(green)(1/2)` Simplify `\text(Factor) =` `2` Now divide the `x`-coordinate in the point `(12,-3)` by
`\text(Factor)=2`.Point `(12,-3)` becomes `(12\divide2,-3)=R(6,-3)`.Method 2To find the original coordinate, take the given x-coordinate `(x=12)` and divide it by the horizontal dilation factor`x/\text(Factor)=12/2=6``R(6,-3)` -
Question 3 of 4
3. Question
When `y=f(x)` is transformed to `y=f(ax)`, the coordinates become `(-18,4)`.
Find the original coordinates `(x,y)` when `a=1/6`.Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilation (stretch/shrink) factor takes the form `y=f(ax)` where the horizontal dilation factor can be found with `\text(Factor) =1/a`.Alternatively, to find the original coordinates you can divide using `x/\text(Factor)`Method 1To find the original coordinates `(x,y)` when `a=1/6` start by finding the transform factor `\text(Factor) =1/a`.`\text(Factor) =` `1/color(green)(1/6)` Simplify `\text(Factor) =` `6` Now divide the `x`-coordinate in the point `(-18,4)` by the Factor (`6`).Point `(-18,4)` becomes `(-18\divide6,4)=(-3,4)`.Method 2To find the original coordinate, take the given x-coordinate `(x=-18)` and divide it by the horizontal dilation (stretch/shrink) factor`x/\text(Factor)=-18/6=-3``(-3,4)` -
Question 4 of 4
4. Question
The point `(-6,3)` lies on `y=f(x)`. Find the coordinates of image `A` on transformed function `y=f(ax)` when `a=1/2`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilation (stretch/shrink) factor takes the form `y=f(ax)` where the horizontal dilation factor can be found with `\text(Factor) =1/a`.Alternatively, to find the image point coordinates, we take the
x-coordinate and multiply by the horizontal dilation factorTo find the coordinates of the image point we take `(-6,4)` when `a=1/2`. We start by finding the horizontal dilation (stretch/shrink) factor using `\text(Factor) =1/a`.`\text(Factor) =` `1/color(green)(1/2)` Simplify `\text(Factor) =` `2` Now multiply the `x`-coordinate for the point `(-6,3)` by the Factor (`2`).Point `(-6,3)` becomes `(-6\times 2,3)=A(-12,3)`.`A(-12,3)`
Quizzes
- Vertical Translations 1
- Vertical Translations 2
- Vertical Translations from a Point
- Horizontal Translations 1
- Horizontal Translations 2
- Horizontal Translations from a Point
- Horizontal Translations from a Graph
- Horizontal and Vertical Translations from a Graph
- Sketch a Graph using Translations
- Write the Equation from a Graph
- Write the Equation from Translations
- Vertical Dilations
- Horizontal Dilations 1
- Horizontal Dilations 2
- Horizontal Dilations – Scale Factor
- Horizontal and Vertical Dilations 1
- Horizontal and Vertical Dilations 2
- Horizontal and Vertical Dilations 3
- Graphing Reflections 1
- Graphing Reflections 2
- Reflection with Rotation
- Combinations of Transformations: Order
- Combinations of Transformations: Coordinates
- Combinations of Transformations: Find Equation 1
- Combinations of Transformations: Find Equation 2
- Combinations of Transformations: Find Equation 3