QUESTION IMAGE
Question
grid with two mitten - shaped figures (one outlined, one shaded) and a grid background; a small scale is present at the top right.
To determine the transformation (translation) of the mitten, we analyze the movement of a key point (e.g., the top - left corner of the mitten's cuff) or the overall shape.
Step 1: Analyze horizontal movement
Let's take a reference point on the original (un - shaded) mitten and the corresponding point on the shaded mitten. Looking at the grid, we can see that the shaded mitten has moved to the right. By counting the number of grid squares, we find that the horizontal (x - direction) movement is 1 unit to the right? Wait, no, let's re - examine. Wait, actually, if we look at the position of the mitten, the original mitten (un - shaded) and the shaded mitten: Let's consider the x - coordinate (horizontal) and y - coordinate (vertical) changes.
Wait, maybe a better way: Let's find the displacement in the x (horizontal) and y (vertical) directions.
Looking at the grid, the un - shaded mitten is at a higher y - level (more towards the top) and the shaded mitten is at a lower y - level (more towards the bottom). Let's count the vertical squares: The un - shaded mitten's main part is from, say, row 2 - 4 (assuming the top row is row 1), and the shaded mitten's main part is from row 6 - 8. So the vertical movement is 4 units down? Wait, no, let's count the number of grid lines. Wait, maybe the grid has each square with side length 1 unit.
Wait, let's take the center of the mitten's palm. For the un - shaded mitten, let's assume its center is at (x1,y1), and for the shaded mitten, its center is at (x2,y2).
Looking at the horizontal (x) direction: The un - shaded mitten is more to the left, and the shaded mitten is more to the right. Let's count the number of squares between the two centers horizontally. If we count, the horizontal displacement is 1 unit to the right? No, wait, maybe I made a mistake. Wait, actually, let's look at the cuff of the mitten. The un - shaded mitten's cuff is at column 5 (assuming columns start from 1 on the left), and the shaded mitten's cuff is at column 6? No, maybe the correct way is:
Wait, the problem is likely to find the translation vector. Let's assume that each grid square is 1 unit.
Looking at the vertical movement: The un - shaded mitten is above the shaded mitten. Let's count the number of units it has moved down. From the top mitten to the bottom mitten, the vertical distance (number of grid squares) is 4 units down. And horizontally, it has moved 1 unit to the right? Wait, no, maybe the horizontal movement is 1 unit to the right and vertical movement is 4 units down. But maybe the question is to find the translation, for example, how many units right and down.
Wait, maybe the correct answer is that the mitten is translated 1 unit to the right and 4 units down. But let's check again.
Wait, looking at the grid, the un - shaded mitten (top) and the shaded mitten (bottom):
- Horizontal (x - axis) movement: Let's take a point on the un - shaded mitten, say the right - most point of the cuff. For the un - shaded mitten, the right - most point of the cuff is at column 5 (if we start counting columns from 1 on the left). For the shaded mitten, the right - most point of the cuff is at column 6. So horizontal movement is + 1 (1 unit to the right).
- Vertical (y - axis) movement: The top of the un - shaded mitten's palm is at row 2 (if we start counting rows from 1 at the top). The top of the shaded mitten's palm is at row 6. So the vertical movement is 6 - 2 = 4 units down (since y - coordinate increases as we go down in a typical grid where top is row 1).
So the translation is 1 unit to the righ…
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
The mitten is translated 1 unit to the right and 4 units down (or in vector form, the translation vector is \((1, - 4)\) if we consider upward as positive y - direction, but if we consider downward as positive y - direction, it's \((1,4)\)). If we are only asked about the vertical or horizontal component, for vertical it's 4 units down, for horizontal it's 1 unit right.