A Dilation is to stretch or to shrink the shape of a curve. Horizontal dilation (stretch/shrink) factor takes the form y=f(ax)y=f(ax) where the horizontal dilation factor can be found with Factor=1aFactor=1a.
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=2a=2 start by finding the horizontal dilation (stretch/shrink) factor Factor=1aFactor=1a.
Factor=Factor=
1212
Simplify
Factor=Factor=
1212
Now multiply the xx-coordinate in each point A(-2,6)A(−2,6) and B(8,0)B(8,0) by the Factor (1212).
Point A(-2,6)A(−2,6) becomes (-2×12,6)=(-1,6)(−2×12,6)=(−1,6).
Then, multiply the xx-coordinate of B(8,0)B(8,0) by the Factor (1212).
Point B(8,0)B(8,0) becomes (8×12,0)=(4,0)(8×12,0)=(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 1212
For A:(-2×12,6)=(-1,6)A:(−2×12,6)=(−1,6)
For B(8×12,0)=(4,0)B(8×12,0)=(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(ax)y=f(ax), the coordinates become (12,-3)(12,−3).
Find the original coordinates of RR when a=12a=12.
A Dilation is to stretch or to shrink the shape of a curve. Horizontal dilation (stretch/shrink) factor takes the form y=f(ax)y=f(ax) where the horizontal dilation factor can be found with Factor=1aFactor=1a.
Alternatively, to find the original coordinates you can divide using xFactorxFactor
Method 1
To find the original coordinates (x,y)(x,y) when a=12a=12. We start by finding the horizontal dilation (stretch/shrink) factor Factor=1aFactor=1a.
Factor=Factor=
112112
Simplify
Factor=Factor=
22
Now divide the xx-coordinate in the point (12,-3)(12,−3) by Factor=2Factor=2.
Point (12,-3)(12,−3) becomes (12÷2,-3)=R(6,-3)(12÷2,−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
xFactor=122=6xFactor=122=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(ax)y=f(ax), the coordinates become (-18,4)(−18,4).
Find the original coordinates(x,y)(x,y) when a=16a=16.
A Dilation is to stretch or to shrink the shape of a curve. Horizontal dilation (stretch/shrink) factor takes the form y=f(ax)y=f(ax) where the horizontal dilation factor can be found with Factor=1aFactor=1a.
Alternatively, to find the original coordinates you can divide using xFactorxFactor
Method 1
To find the original coordinates (x,y)(x,y) when a=16a=16 start by finding the transform factor Factor=1aFactor=1a.
Factor=Factor=
116116
Simplify
Factor=
6
Now divide the x-coordinate in the point (-18,4) by the Factor (6).
Point (-18,4) becomes (-18÷6,4)=(-3,4).
Method 2
To find the original coordinate, take the given x-coordinate (x=-18) and divide it by the horizontal dilation (stretch/shrink) factor
xFactor=-186=-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=12.
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 Factor=1a.
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) when a=12. We start by finding the horizontal dilation (stretch/shrink) factor using Factor=1a.
Factor=
112
Simplify
Factor=
2
Now multiply the x-coordinate for the point (-6,3) by the Factor (2).
