Perform the second translation on the image of the first translation.
Practice makes perfect
We want to use the given translations to find the image â–łX''Y''Z''. We should begin by plotting the endpoints of the preimage, X(2,4), (6,0), and Z(7,2), on a coordinate plane.
Next, we can do the first of the given translations, (x,y) → (x-6,y). This translation tells us that we should subtract 6 from the x-coordinates, and the y-coordinates have no change.
ccc
(x,y) &→ & (x-6,y)
X(2,4) &→ & X'(-4,4)
Y(6,0) &→ & Y'(0,0)
Z(7,2) &→ & Z'(1,2)
Let's add these new points to the same coordinate plane and draw â–ł X'Y'Z'.
Now, we can translate the new image, â–łX'Y'Z', using the second of the given translations.
ccc
(x,y) &→ & (x+2,y+7)
X'(-4,4) &→ & X''(-2,11)
Y'(0,0) &→ & Y''(2,7)
Z'(1,2) &→ & Z''(3,9)
We can use these new coordinates to draw the image â–łX''Y''Z''.
We can remove the intermediate image so that we can see only the preimage and the image after the composition of the translations.
