Before we attempt to translate the given points, let's draw the triangle â–ł XYZ on a coordinate plane using the given points.
We can now draw segments between the points to form the triangle.
Now that we have the preimage, we can create the image using the translation (x,y) → (x+3,y-1). This translation tells us that for every point in △ XYZ, we should add 3 to the x-coordinate and subtract 1 from the y-coordinate.
ccc
(x,y) &→ &(x+3,y-1)
X(2,3) &→ & X'(5,2)
Y(-3,2) &→ & Y'(0,1)
Z(-4,-3) &→ & Z'(-1,-4)
Now we have the points for the image. Let's add them to the same coordinate plane as the preimage.
We can see that the translation moved the points to the right and down. Finally, we can connect the points to have the new triangle.
