Which figure is a translation of Figure 1?
The Correct Answer and Explanation is:
The correct answer is Figure B.
Explanation
A translation in geometry means moving a shape without rotating, flipping, or changing its size or orientation. The figure remains exactly the same in shape and direction, but its location on the coordinate grid changes.
Let’s examine Figure 1 carefully. Figure 1 is located in the bottom-left part of the grid, positioned between x = 0 to x = 2 and y = 1 to y = 3. Its defining characteristic is a “<” shape opening to the left.
Now, let’s analyze the other figures:
- Figure A is positioned above Figure 1 and has the same shape and size. However, the orientation of the figure is different—it opens to the right, not to the left. This indicates a rotation or reflection, not a translation.
- Figure C is located directly to the right of Figure 1, and while it is in the same general position as a translation might be, its orientation is incorrect. The “V” shape faces downward instead of the left. So again, this is not a translation—it is a rotation or flip.
- Figure B, however, maintains the exact same shape and orientation as Figure 1—it still has the “<” shape opening to the left. Moreover, the only difference is its location. Figure B is translated (moved) rightward and upward compared to Figure 1. Specifically, it appears to be moved 4 units to the right and 2 units up, from its original position.
Since Figure B is identical in size, shape, and direction to Figure 1 and has only been shifted in position, it is the correct translation.
Thus, the figure that is a translation of Figure 1 is Figure B.
