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–³ X''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 perform the first of the given translations, (x,y) → (x+12,y+4). This translation tells us that we should add 12 to the x-coordinates and 4 to the y-coordinates.
ccc
(x,y) &→ & (x+12,y+4)
X(2,4) &→ & X'(14,8)
Y(6,0) &→ & Y'(18,4)
Z(7,2) &→ & Z'(19,6)
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–³ X'Y'Z', using the second of the given translations.
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(x,y) &→ & (x-5,y-9)
X'(14,8) &→ & X''(9,-1)
Y'(18,4) &→ & Y''(13,-5)
Z'(19,6) &→ & Z''(14,-3)
We can use these new coordinates to draw the image â–³ X''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.
