To graph J''K''L''M'' you have to perform a translation. To graph JKLM you have to undo a dilation.
JKLM and J''K''L''M'' are similar.
JKLM: (-8,0), (-8,12), (-4,12), (-4,0)
J''K''L''M'': (-9,-4), (-9,14), (-3,14), (-3,-4)
Practice makes perfect
Let's first determine if JKLM and J''K''L''M'' are similar. A translation is a rigid motion which means angle and side measures are preserved. Therefore, we can say that
J'K'L'M' and J''K''L''M''
are similar as they will have the same shape and size after performing the translation. Additionally, a dilation changes a figure's size but not its shape. Since similar figures only need to have the same shape, we can also say that
JKLM and J'K'L'M'
are similar. Since J'K'L'M' is simlar to both its preimage and its image, we must have that
JKLM and J''K''L''M''
are similar.
Coordinates of preimage and image
Let's begin by graphing J'K'L'M' for which we have the coordinates.
Now we can proceed with finding the coordinates of the image, J''K''L''M'', and the preimage, JKLM.
Preimage
The image of J'K'L'M' was created by dilating the preimage, JKLM, with a scale factor of 32=1.5. Therefore, to go from J'K'L'M' to JKLM we have to undo this dilation. We can do that by dilating the coordinates of J'K'L'M with a scale factor of 11.5.
Point
(a,b)
(1/1.5a,1/1.5b)
J'
(- 12,0)
(- 8,0)
K'
(- 12,18)
(- 8,12)
L'
(- 6,18)
(- 4,12)
M'
(- 6,0)
(- 4,0)
When we know the coordinates of JKLM, we can draw this rectangle.
Image
The image of J''K''L''M'' was created by translating the preimage, J'K'L'M' using a translation.
(x,y)→ (x+3,y-4)
To perform the translation we should go 3 units to the right and 4 units down.
Point
(a,b)
(a+3,b-4)
J'
(- 12,0)
(- 9,- 4)
K'
(- 12,18)
(- 9,14)
L'
(- 6,18)
(- 3,14)
M'
(- 6,0)
(- 3,- 4)
When we know the coordinates of J''K''L''M'', we can draw this rectangle.
