Coordinate Plane Translations: Mapping Figures on a Grid

To determine the translation that maps Figure B onto Figure C, we need to pick a corresponding point on each figure and find the change in its coordinates.

Let’s identify the coordinates of the vertices of Figure B and Figure C.

Figure B vertices:
Let’s pick the top-leftmost vertex of Figure B. Its coordinates are approximately .
Let’s pick the bottom-leftmost vertex of Figure B. Its coordinates are approximately .
Let’s pick the top-rightmost vertex of Figure B. Its coordinates are approximately .
Let’s pick the bottom-rightmost vertex of Figure B. Its coordinates are approximately .

Figure C vertices:
Let’s pick the top-leftmost vertex of Figure C. Its coordinates are approximately .
Let’s pick the bottom-leftmost vertex of Figure C. Its coordinates are approximately .
Let’s pick the top-rightmost vertex of Figure C. Its coordinates are approximately .
Let’s pick the bottom-rightmost vertex of Figure C. Its coordinates are approximately .

Now, let’s choose a corresponding point from Figure B and Figure C. Let’s take the top-leftmost vertex of Figure B, which is , and its corresponding point in Figure C, which is .

To find the translation, we subtract the coordinates of the initial point (from Figure B) from the coordinates of the final point (from Figure C).

Change in x-coordinate:
Change in y-coordinate:

So, the translation is 4 units to the right and 6 units down.

Let’s verify this with another pair of corresponding points.
Consider the bottom-leftmost vertex of Figure B: .
Its corresponding point in Figure C is .

Change in x-coordinate:
Change in y-coordinate:

The translation is consistent: 4 units to the right and 6 units down.

The final answer is .