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Horizontal Dilations (Stretch/Shrink)>
Horizontal Dilations (Stretch/Shrink) 1Horizontal Dilations (Stretch/Shrink) 1
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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=1/4`.
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 factorTo find the image points for `A(-2,6)` and `B(8,0)` when `a=1/4`. We start by finding the horizontal dilation (stretch/shrink) factor:
`\text(Factor) =1/a`.`\text(Factor) =` `1/color(green)(1/4)` Simplify `\text(Factor) =` `4` Now multiply the `x`-coordinate in the points `A(-2,6)` and `B(8,0)` by the Factor (`4`).Point `(-2,6)` becomes `(-2\times 4,6)=(-8,6)`.Then, multiply the `x`-coordinate of `B(8,0)` by the Factor (`4`).Point `B(8,0)` becomes `(8\times 4,0)=(32,0)`.`A(-8,6)` and `B(32,0)` -
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=3`.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)`To find the original coordinates `(x,y)` when `a=3`. We start by finding the horizontal dilation (stretch/shrink) factor
`\text(Factor) =1/a`.`\text(Factor) =` `color(green)(1/3)` Now divide the `x`-coordinate for the point `(12,-3)` by the `\text(Factor)=1/3`.Point `(12,-3)` becomes `(12\divide 1/3,-3)=(36,-3)`.`(36,-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=3`.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)`To find the original coordinates `(x,y)` when `a=3`. We start by finding the horizontal dilation (stretch/shrink) factor
`\text(Factor) =1/a`.`\text(Factor) =` `1/color(green)(3)` Simplify `\text(Factor) =` `1/3` Now divide the `x`-coordinate in the point `(-18,4)` by the Factor of `1/3`.Point `(-18,4)` becomes `(-18 \divide 1/3,4)=(-54,4)`.`(-54,4)` -
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`.
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)` Simplify `\text(Factor) =` `-1` Now multiply the `x`-coordinate in each point `A(-6,3)` by the Factor (`-1`).Point `A(-6,3)` becomes `(-6\times -1,3)=(6,3)`.`A(6,3)`
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