Translations are done by adding or subtracting values from the x-coordinate if the figure is being moved left or right, and from the y-coordinate if the figure is being moved up or down.
Practice makes perfect
We are given the vertices of triangle FGH. We will start by graphing this points and connect them to form â–ł FGH.
We want to find the image of this triangle after a similarity transformation. Let's do one transformation at time!
Translation
Translations are done by adding or subtracting values from the x-coordinate if the figure is being moved left or right, and from the y-coordinate if the figure is being moved up or down. We want to draw the image of our figure after a translation of 3 units to the right and 1 unit up. Therefore, we will add 3 to the x-coordinate and add 1 to the y-coordinate of each vertex.
Vertices of FGH
(x+3,y+1)
Vertices of F'G'H'
F(- 2,2)
(- 2 + 3,2 + 1)
F'(1,3)
G(- 2,- 4)
(- 2 + 3,- 4 + 1)
G'(1,- 3)
H(- 4,- 4)
(- 4 + 3,- 4 + 1)
H'(- 1,- 3)
Let's do the translation!
Dilation
A dilation can be an enlargement, a reduction, or the same size as the preimage. Which type of dilation it is depends on the value of the scale factor k.
Enlargement
k>1
Reduction
0
Same
k=1
When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Now, let's find the coordinates of the vertices of F'G'H' after a dilation with a scale factor k= 2.
Dilation With Scale Factor k=2
Preimage
Multiply by k
Image
F'(1,3)
( 2 (1), 2 (3))
F''(2,6)
G'(1,- 3)
( 2 (1), 2 (- 3))
G''(2,- 6)
H'(- 1,- 3)
( 2 (- 1), 2 (- 3))
H''(- 2,- 6)
We can now plot the obtained points and connect them with segments to draw the image.
Finally, we will remove â–ł F'H'G' from the coordinate plane.
