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–³X''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–³ X'Y'Z'.
Now, we can translate the new image, â–³X'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–³X''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.
