Question

describe the translation from the shaded figure to the unshaded figure. the shaded figure is translated 3 units to the right and blank units blank

Explanation:

Step1: Identify vertical translation

Find the vertical distance between corresponding vertices (e.g., the bottom vertex of the shaded triangle is at \( y = -6 \), unshaded at \( y = -2 \)). The difference is \( -2 - (-6) = 4 \), so 4 units up.

Step2: Confirm horizontal translation

Horizontal distance: shaded vertex at \( x = -3 \), unshaded at \( x = 5 \). \( 5 - (-3) = 8 \)? Wait, no—wait, the grid: shaded triangle's bottom left is at \( x=-4, y=-6 \)? Wait, no, let's recheck. Wait, the shaded triangle: let's take the top vertex. Shaded top at \( x=-3, y=-1 \)? No, wait the unshaded top is at \( x=5, y=3 \). Wait, maybe better to take the bottom base. Shaded bottom base: from \( x=-4 \) to \( x=-2 \) (so center at \( x=-3 \)), \( y=-6 \). Unshaded bottom base: from \( x=4 \) to \( x=6 \), center at \( x=5 \), \( y=-2 \). So horizontal change: \( 5 - (-3) = 8 \)? Wait, no, the initial box has "3" but that's wrong. Wait, maybe I misread. Wait, the user's initial input has a box with "3" but maybe that's a mistake. Wait, no—wait, let's calculate correctly. Shaded triangle: let's take the top vertex. Shaded top: \( (-3, -1) \)? No, looking at the grid, shaded triangle: the top is at \( (-3, -1) \)? Wait, no, the y-axis: the shaded triangle is below the x-axis, from y=-1 to y=-6? Wait, no, the grid lines: each grid is 1 unit. Shaded triangle: bottom at y=-6, top at y=-1 (so height 5). Unshaded triangle: bottom at y=-2, top at y=3 (height 5). So vertical translation: from y=-6 to y=-2: that's 4 units up (since -2 - (-6) = 4). Horizontal: shaded bottom center at x=-3, unshaded at x=5. So 5 - (-3) = 8? Wait, no, the initial box has "3" but that's incorrect. Wait, maybe the shaded triangle's top is at (-3, -1) and unshaded at (5, 3). So horizontal: 5 - (-3) = 8? No, wait, maybe the user's initial input has a typo, but let's check the vertical. From y=-6 (shaded bottom) to y=-2 (unshaded bottom): 4 units up. So the correct vertical translation is 4 units up, and horizontal: let's see, shaded left bottom corner: (-4, -6), unshaded left bottom: (4, -2). So horizontal: 4 - (-4) = 8? No, that's not. Wait, maybe I made a mistake. Wait, the unshaded triangle: bottom base is from x=4 to x=6 (so length 2), same as shaded (x=-4 to x=-2, length 2). So shaded bottom left: (-4, -6), unshaded bottom left: (4, -2). So horizontal change: 4 - (-4) = 8? No, that's 8 units right. Vertical change: -2 - (-6) = 4 units up. But the initial box has "3" which is wrong. Wait, maybe the problem's grid is different. Wait, maybe the shaded triangle's top is at (-3, -1) and unshaded at (5, 3). So x: 5 - (-3) = 8, y: 3 - (-1) = 4. So translation is 8 units right and 4 units up. But the user's initial input has a box with "3"—maybe that's a mistake. But according to the grid, let's re-express:

Shaded triangle: let's take a vertex, say the bottom left corner: (-4, -6). Unshaded bottom left: (4, -2). So horizontal shift: 4 - (-4) = 8 (right), vertical shift: -2 - (-6) = 4 (up). So the correct translation is 8 units right and 4 units up. But maybe the user's problem has a different grid. Wait, maybe I misread the x-coordinates. Let's check the x-axis: from -5 to 5, with ticks at -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Shaded triangle: bottom base between x=-4 and x=-2 (so x=-4, -3, -2), y=-6. Unshaded triangle: bottom base between x=4 and x=6 (x=4, 5, 6), y=-2. So the center of the bottom base: shaded at x=-3, y=-6; unshaded at x=5, y=-2. So horizontal distance: 5 - (-3) = 8 (right), vertical distance: -2 - (-6) = 4 (up). So the translation is 8 units to the right and 4 units up. But the initial box has "3"—maybe that's an error. Assuming the vertical translation: from y=-6 to y=-2 is 4 units up. So the missing part: 4 units up.

Answer:

The shaded figure is translated 8 units to the right and 4 units up. (Note: If the initial "3" is correct, there's a discrepancy, but based on grid analysis, vertical is 4 up, horizontal 8 right.)