Horizontal Dilations (Stretch/Shrink) 2

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Question 1 of 4

1. Question
The points $A (- 2, 6)$ $A(-2,6)$ and $B (8, 0)$ $B(8,0)$ lie on $y = f (x)$ $y=f(x)$ . Find the coordinates of images $A$ $A$ and $B$ $B$ for $y = f (a x)$ $y=f(ax)$ when $a = 2$ $a=2$ .
- 1. $A (4, 0)$ $A(4,0)$ and $B (- 1, 6)$ $B(-1,6)$
- 2. $A (1, - 6)$ $A(1,-6)$ and $B (4, 0)$ $B(4,0)$
- 3. $A (- 1, 6)$ $A(-1,6)$ and $B (4, 0)$ $B(4,0)$
- 4. $A (- 1, - 6)$ $A(-1,-6)$ and $B (- 4, 0)$ $B(-4,0)$
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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 $y = f (a x)$ $y=f(ax)$ where the horizontal dilation factor can be found with $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

Alternatively, to find the image point coordinates, we take the
x-coordinate and multiply by the horizontal dilation factor

Method 1

To find the image points for $A (- 2, 6)$ $A(-2,6)$ and $B (8, 0)$ $B(8,0)$ when $a = 2$ $a=2$ start by finding the horizontal dilation (stretch/shrink) factor $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

$Factor =$ $\text(Factor) =$ $\frac{1}{2}$ $1/color(green)(2)$ Simplify

$Factor =$ $\text(Factor) =$ $\frac{1}{2}$ $1/2$

Now multiply the $x$ $x$ -coordinate in each point $A (- 2, 6)$ $A(-2,6)$ and $B (8, 0)$ $B(8,0)$ by the Factor ( $\frac{1}{2}$ $1/2$ ).

Point $A (- 2, 6)$ $A(-2,6)$ becomes $(- 2 \times \frac{1}{2}, 6) = (- 1, 6)$ $(-2 xx 1/2,6)=(-1,6)$ .

Then, multiply the $x$ $x$ -coordinate of $B (8, 0)$ $B(8,0)$ by the Factor ( $\frac{1}{2}$ $1/2$ ).

Point $B (8, 0)$ $B(8,0)$ becomes $(8 \times \frac{1}{2}, 0) = (4, 0)$ $(8 xx 1/2,0)=(4,0)$ .

Method 2

To find the image points all you have to do is take the x-coordinates $A (x = - 2)$ $A(x=-2)$ and for $B (x = 8)$ $B(x=8)$ and multiply each of them by the horizontal dilation factor of $\frac{1}{2}$ $1/2$

For $A : (- 2 \times \frac{1}{2}, 6) = (- 1, 6)$ $A:(-2 xx 1/2, 6)=(-1,6)$

For $B (8 \times \frac{1}{2}, 0) = (4, 0)$ $B(8 xx 1/2,0)=(4,0)$

$A (- 1, 6)$ $A(-1,6)$ and $B (4, 0)$ $B(4,0)$
Question 2 of 4

2. Question
When $y = f (x)$ $y=f(x)$ is transformed to $y = f (a x)$ $y=f(ax)$ , the coordinates become $(12, - 3)$ $(12,-3)$ .
Find the original coordinates of $R$ $R$ when $a = \frac{1}{2}$ $a=1/2$ .
- 1. $(6, - 3)$ $(6,-3)$
- 2. $(24, - 3)$ $(24,-3)$
- 3. $(8, - 3)$ $(8,-3)$
- 4. $(12, - 3)$ $(12,-3)$
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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 $y = f (a x)$ $y=f(ax)$ where the horizontal dilation factor can be found with $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

Alternatively, to find the original coordinates you can divide using $\frac{x}{Factor}$ $x/\text(Factor)$

Method 1

To find the original coordinates $(x, y)$ $(x,y)$ when $a = \frac{1}{2}$ $a=1/2$ . We start by finding the horizontal dilation (stretch/shrink) factor
$Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

$Factor =$ $\text(Factor) =$ $\frac{1}{\frac{1}{2}}$ $1/color(green)(1/2)$ Simplify

$Factor =$ $\text(Factor) =$ $2$ $2$

Now divide the $x$ $x$ -coordinate in the point $(12, - 3)$ $(12,-3)$ by
$Factor = 2$ $\text(Factor)=2$ .

Point $(12, - 3)$ $(12,-3)$ becomes $(12 \div 2, - 3) = R (6, - 3)$ $(12\divide2,-3)=R(6,-3)$ .

Method 2

To find the original coordinate, take the given x-coordinate $(x = 12)$ $(x=12)$ and divide it by the horizontal dilation factor

$\frac{x}{Factor} = \frac{12}{2} = 6$ $x/\text(Factor)=12/2=6$

$R (6, - 3)$ $R(6,-3)$
Question 3 of 4

3. Question
When $y = f (x)$ $y=f(x)$ is transformed to $y = f (a x)$ $y=f(ax)$ , the coordinates become $(- 18, 4)$ $(-18,4)$ .
Find the original coordinates $(x, y)$ $(x,y)$ when $a = \frac{1}{6}$ $a=1/6$ .
- 1. $(- 18, \frac{2}{3})$ $(-18,2/3)$
- 2. $(- 18, 10)$ $(-18,10)$
- 3. $(- 12, 4)$ $(-12,4)$
- 4. $(- 3, 4)$ $(-3,4)$
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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 $y = f (a x)$ $y=f(ax)$ where the horizontal dilation factor can be found with $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

Alternatively, to find the original coordinates you can divide using $\frac{x}{Factor}$ $x/\text(Factor)$

Method 1

To find the original coordinates $(x, y)$ $(x,y)$ when $a = \frac{1}{6}$ $a=1/6$ start by finding the transform factor $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

$Factor =$ $\text(Factor) =$ $\frac{1}{\frac{1}{6}}$ $1/color(green)(1/6)$ Simplify

$Factor =$ $\text(Factor) =$ $6$ $6$

Now divide the $x$ $x$ -coordinate in the point $(- 18, 4)$ $(-18,4)$ by the Factor ( $6$ $6$ ).

Point $(- 18, 4)$ $(-18,4)$ becomes $(- 18 \div 6, 4) = (- 3, 4)$ $(-18\divide6,4)=(-3,4)$ .

Method 2

To find the original coordinate, take the given x-coordinate $(x = - 18)$ $(x=-18)$ and divide it by the horizontal dilation (stretch/shrink) factor

$\frac{x}{Factor} = - \frac{18}{6} = - 3$ $x/\text(Factor)=-18/6=-3$

$(- 3, 4)$ $(-3,4)$
Question 4 of 4

4. Question
The point $(- 6, 3)$ $(-6,3)$ lies on $y = f (x)$ $y=f(x)$ . Find the coordinates of image $A$ $A$ on transformed function $y = f (a x)$ $y=f(ax)$ when $a = \frac{1}{2}$ $a=1/2$ .
- 1. $A (- 12, 3)$ $A(-12,3)$
- 2. $A (3, 3)$ $A(3,3)$
- 3. $A (- 3, 3)$ $A(-3,3)$
- 4. $A (12, 3)$ $A(12,3)$
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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 $y = f (a x)$ $y=f(ax)$ where the horizontal dilation factor can be found with $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

Alternatively, to find the image point coordinates, we take the
x-coordinate and multiply by the horizontal dilation factor

To find the coordinates of the image point we take $(- 6, 4)$ $(-6,4)$ when $a = \frac{1}{2}$ $a=1/2$ . We start by finding the horizontal dilation (stretch/shrink) factor using $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

$Factor =$ $\text(Factor) =$ $\frac{1}{\frac{1}{2}}$ $1/color(green)(1/2)$ Simplify

$Factor =$ $\text(Factor) =$ $2$ $2$

Now multiply the $x$ $x$ -coordinate for the point $(- 6, 3)$ $(-6,3)$ by the Factor ( $2$ $2$ ).

Point $(- 6, 3)$ $(-6,3)$ becomes $(- 6 \times 2, 3) = A (- 12, 3)$ $(-6\times 2,3)=A(-12,3)$ .

$A (- 12, 3)$ $A(-12,3)$

Horizontal Dilations (Stretch/Shrink) 2

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Quizzes

$Factor =$ $\text(Factor) =$		$\frac{1}{2}$ $1/color(green)(2)$	Simplify
$Factor =$ $\text(Factor) =$		$\frac{1}{2}$ $1/2$

$Factor =$ $\text(Factor) =$		$\frac{1}{\frac{1}{2}}$ $1/color(green)(1/2)$	Simplify
$Factor =$ $\text(Factor) =$		$2$ $2$

$Factor =$ $\text(Factor) =$		$\frac{1}{\frac{1}{6}}$ $1/color(green)(1/6)$	Simplify
$Factor =$ $\text(Factor) =$		$6$ $6$