We want to use the given translations to find the image $\overline{V^{''} W^{''}} .$ We should begin by plotting the endpoints of the preimage, $V (- 6, - 4)$ and $W (- 3, 1),$ on a coordinate plane.

Next, we can do the first of the given translations,

(x, y) \to (x + 3, y + 1) .

This translation tells us that we should add

3

to the

x -

coordinates and

1

to the

y -

coordinates.

(x, y) V (- 6, - 4) W (- 3, 1) \to \to \to (x + 3, y + 1) V^{'} (- 3, - 3) W^{'} (0, 2)

Let's add these new points to the same coordinate plane.

Now, we can translate the new image,

\overline{V^{'} W^{'}},

using the second of the given translations,

(x, y) \to (x - 6, y - 4) .

We need to subtract

6

from the

x -

coordinates and

4

from the

y -

coordinates.

(x, y) V^{'} (- 3, - 3) W^{'} (0, 2) \to (x - 6, y - 4) \to V^{''} (- 9, - 7) \to W^{''} (- 6, - 2)

Finally, we can use these new coordinates to draw the image

\overline{V^{''} W^{''}} .

We can remove the intermediate image so that we can see only the preimage and the image after the composition of the translations.

{{ 'ml-heading-exercise' | message }} {{ exercise.name }} {{ 'ml-label-page' | message }} {{ exercise.page }}

{{ 'ml-solutions-missing-heading' | message }}