Question

which of the number figures are translations of the shaded figure?

Explanation:

Step1: Recall translation definition

A translation is a rigid transformation that slides a figure without rotating or reflecting it, so the shape, size, and orientation remain the same.

Step2: Analyze each figure

- **Figure 5**: Compare with shaded figure. Check shape, orientation. The shaded figure has a specific L - shape with a "notch" on the top - right. Figure 5 has the same shape and orientation, just moved.
- **Figure 6**: Check orientation. The shaded figure's "notch" is on the top - right, Figure 6's "notch" is on the top - left (reflected or rotated? No, wait, actually, when we look at the grid, Figure 6: Let's check the relative positions of the squares. The shaded figure has a horizontal part and a vertical part. Figure 6: The horizontal part and vertical part are in the same relative proportion and orientation as the shaded figure? Wait, no, maybe I made a mistake. Wait, let's re - examine.
Wait, the shaded figure: Let's count the number of squares and their arrangement. The shaded figure has a base of 3 squares (horizontal) and a vertical part of 2 squares with a notch of 1 square missing on the top - right. Now, Figure 5: Let's see, it has the same arrangement. Figure 8: Wait, the arrow on Figure 8 is a translation? Wait, no, the question is which number figures are translations of the shaded figure.
Wait, let's list the figures:
- Shaded figure: Let's define its shape. It's an L - shape with a "cut" on the top - right. So the figure has a horizontal segment (length 3) and a vertical segment (length 2) with a 1 - square indentation on the top - right of the vertical segment.
- Figure 5: Same shape, same orientation, just moved. So it's a translation.
- Figure 8: Wait, the arrow on Figure 8 is a translation? Wait, Figure 8's shape: Let's check. The horizontal part and vertical part. Wait, maybe I misidentified. Wait, let's check each figure:
1. Figure 1: Orientation is different (rotated? Maybe 90 degrees? So not a translation).
2. Figure 2: Orientation is different (maybe rotated 180? No, translation preserves orientation).
3. Figure 3: Orientation is different.
4. Figure 4: Orientation is different.
5. Figure 5: Same shape, same orientation, so translation.
6. Figure 6: Wait, Figure 6: Let's see, the indentation is on the top - left? No, maybe it's a reflection? No, translation doesn't reflect. Wait, maybe Figure 5, Figure 8? Wait, no, the arrow on Figure 8 is a translation direction? Wait, the original shaded figure: Let's count the grid positions. The shaded figure is at some position. Figure 5: If we move the shaded figure left and down (or some translation vector), it matches Figure 5. Figure 8: Wait, Figure 8's shape: Let's check the number of squares. The shaded figure has, let's count: horizontal part: 3 squares, vertical part: 2 squares, with a 1 - square indentation. So total squares: 3 + 2 - 1=4? Wait, no, let's count the shaded figure: The shaded figure has a horizontal rectangle of 3 squares (width 3, height 1) and a vertical rectangle of 2 squares (width 1, height 2) attached to the right - hand side of the horizontal rectangle, but with the top - most square of the vertical rectangle missing. So total squares: 3 (horizontal) + 1 (vertical, bottom) = 4? Wait, no, looking at the grid, the shaded figure: Let's see the cells. The shaded figure covers: Let's say the bottom - left cell of the shaded figure is at (x,y), then it has cells (x,y), (x + 1,y), (x + 2,y), (x + 2,y + 1). So that's 4 cells. Now Figure 5: Let's check its cells. It has cells that form the same shape: horizontal 3, vertical 1 (with the top of vertical missing). So Figure 5 is a translation. Figure 8: Let's check its cells. The arrow is pointing up, but the shape of Figure 8: Does it have the same 4 - cell shape? Let's see, Figure 8 has a horizontal part (length 3) and a vertical part (length 2) with a notch? Wait, no, maybe I was wrong. Wait, the correct translations should be figures that have the same shape, size, and orientation as the shaded figure, just moved. So Figure 5, Figure 8? Wait, no, let's re - look. The shaded figure: when we look at Figure 5, it's the same shape, same orientation. Figure 8: The arrow is a translation (maybe moved down and left). Wait, maybe the answer is 5, 8? Wait, no, let's check the original problem again. The shaded figure is at the top - right. Figure 5 is at the top - left, same shape. Figure 8 is below, same shape? Wait, maybe I made a mistake in counting. Alternatively, maybe the correct figures are 5, 8? Wait, no, let's think again. A translation is a slide, so the figure should look exactly the same, just shifted. So the shaded figure has a "notch" on the top - right of its vertical part. So Figure 5: same notch position (top - right of vertical part), same shape. Figure 8: Let's see, the notch is on the top - right? Wait, Figure 8's vertical part: the notch is on the top - left? No, maybe I'm confused. Wait, maybe the correct answer is 5, 8? Or maybe 5, 6, 8? No, let's check each figure:

- Figure 1: Rotated (90 degrees), not translation.
- Figure 2: Rotated (180 degrees), not translation.
- Figure 3: Rotated, not translation.
- Figure 4: Rotated, not translation.
- Figure 5: Same shape, same orientation, translation.
- Figure 6: Same shape? Wait, Figure 6 has a notch on the top - left of its vertical part, which is a reflection of the shaded figure's notch (top - right), so not translation.
- Figure 7: Different shape (more squares), not translation.
- Figure 8: Same shape, same orientation, translation (moved down and left).
- Figure 9: Different shape (more complex), not translation.
- Figure 10: Different shape, not translation.

Answer:

5, 8 (assuming these are the figures with the same shape, size, and orientation as the shaded figure after translation)