Question

name that t can you describe the transformations that would tr figure (pre - image) to the yellow #3

Explanation:

Step1: Analyze Reflection

Check if the pink figure (pre - image) can be reflected over a line to get the yellow figure. A reflection over the y - axis would change the x - coordinates' sign. Let's assume the pink figure has vertices, for example, if a vertex of the pink figure is at (3, 3), after reflection over y - axis, it would be (- 3, 3), which is close to the yellow figure's position.

Step2: Analyze Translation (Optional)

After reflection, we might need a vertical translation. If the reflected figure from the pink one over y - axis is then moved down (since the yellow figure is lower in y - coordinate), say 2 units down. Or we can also consider rotation, but reflection followed by translation seems more likely. Another way: First, reflect the pink figure over the y - axis. Then, translate it down by some units (let's check the grid). The pink figure is in the first quadrant (relative to the grid), the yellow is in the second quadrant (left of y - axis) and lower. So reflection over y - axis and then translation down (or a combination of reflection and translation, or also rotation? Wait, the shape is an L - shape. Let's check the orientation. The pink L is opening to the left? Wait no, the pink L: looking at the grid, the pink figure has a horizontal part to the right and vertical part down? Wait the yellow figure: horizontal part to the left and vertical part down? Wait maybe a reflection over the y - axis and then a translation down. Alternatively, rotation: 180 - degree rotation? But 180 - degree rotation would flip both x and y. But let's see the coordinates. Let's take a key point of the pink figure: say the top - right corner of the pink L is at (4, 3). After reflection over y - axis, it's (- 4, 3), then translating down 2 units: (- 4, 1), which is close to the yellow figure's top - right (or top - left) corner. Wait maybe the correct transformation is: Reflect the pink figure over the y - axis, then translate it down by 2 units (or other number, but mainly reflection and translation). Or also, we can consider that the pink figure can be reflected over the y - axis and then translated vertically. Another approach: The two figures are congruent, so it's a rigid transformation (reflection, rotation, translation). The orientation: the pink L and yellow L: if we reflect over y - axis, the horizontal arm of the L (the top part) which is to the right in pink, becomes to the left in yellow (after reflection), and then it's moved down. So the transformations are: First, reflect the pink figure (pre - image) over the y - axis. Then, translate the reflected figure down by 2 units (or whatever the grid shows, maybe 2 units). Or we can also say a rotation of 180 degrees? Wait no, 180 - degree rotation would make the L open in the opposite direction both horizontally and vertically. But the yellow L and pink L: the vertical arm is down in both? Wait the pink L: vertical arm is down (from y = 3 to y = 5? Wait no, the grid: x - axis is vertical (wait wait, wait the axes: the x - axis is vertical (pointing down) and y - axis is horizontal (pointing right)? Wait maybe I got the axes wrong. Oh! Wait the axes: the x - axis is vertical (arrow down) and y - axis is horizontal (arrow right). So the coordinates: x is vertical, y is horizontal. So a point (x, y) where x is the vertical coordinate (down is positive x?) Wait no, standard coordinate system: x - axis horizontal (left - right), y - axis vertical (up - down). But in the given graph, the x - axis arrow is down, y - axis arrow is right. So it's a rotated coordinate system? Wait maybe the x - axis is vertical (positive down) and y - axis is horizontal (positive right). So let's re - define: Let's say the y - axis is horizontal (right is positive y), x - axis is vertical (down is positive x). So the pink figure is at y from 2 to 4 (horizontal) and x from 3 to 5 (vertical). The yellow figure is at y from - 4 to - 2 (horizontal) and x from 3 to 5 (vertical)? No, the yellow figure is on the left side. Wait maybe the axes are standard, but the graph is drawn with x - axis vertical (down) and y - axis horizontal (right). So to correct, in standard terms, let's rotate the graph 90 degrees clockwise. Then x - axis is horizontal (right), y - axis is vertical (up). Then the pink figure is in the first quadrant (x positive, y positive), yellow in the second quadrant (x positive, y negative? No, wait after rotating the graph 90 degrees clockwise, the original x - axis (down) becomes new y - axis (up), original y - axis (right) becomes new x - axis (right). So maybe it's better to look at the shape: the pink L and yellow L. The pink L has a horizontal segment to the right and vertical segment down (in the original graph's orientation), the yellow L has horizontal segment to the left and vertical segment down. So reflection over the y - axis (which in original graph is the vertical line x = 0, but in the graph, the y - axis is horizontal? Wait I think I messed up the axes. Let's forget the axes labels for a second. The two L - shaped figures: one is pink, one is yellow. The pink is on the right side of the y - axis (the vertical line in the middle), yellow on the left. The pink L is above the yellow L? No, yellow is below? Wait the grid: the x - axis (arrow down) has numbers 0,1,2,...6 (downward), y - axis (arrow right) has numbers 0,1,2,...6 (rightward). So a point's coordinates: (x, y) where x is the vertical position (down is positive x), y is horizontal position (right is positive y). So the pink figure: let's take the top - most point (lowest x - value, since x increases down) of the pink L: x = 3, y = 2 (wait no, x is down, so x = 3 is lower than x = 2). Wait this is confusing. Alternatively, the two figures are congruent, so the transformation is a reflection over the y - axis (the vertical line in the middle of the grid) and then a translation down (since the yellow figure is lower in the x - direction, which is down). So the steps: 1. Reflect the pink figure over the y - axis (the vertical line x = 0, but in the graph, the y - axis is the vertical line with x = 0, y from 0 to 6). 2. Translate the reflected figure down (in the x - direction) by 2 units (or whatever the grid shows, but visually, the yellow figure is 2 units below the reflected pink figure). Or another way: Rotate the pink figure 180 degrees around the origin? But 180 - degree rotation would flip both x and y. But the shape's orientation: after 180 - degree rotation, the L would open in the opposite direction both horizontally and vertically. But the two Ls: the pink L and yellow L: the vertical arm is down in both, horizontal arm: pink to the right, yellow to the left. So reflection over y - axis (flips horizontal direction) and then translation down (flips vertical position? No, translation down moves it lower). So the transformation is: Reflect the pink figure (pre - image) over the y - axis, then translate it down by 2 units (or a combination of reflection and translation, or also, we can say that it's a reflection over the y - axis and a vertical translation (since in standard coordinates, y is vertical, but here the axes are rotated, so maybe it's a horizontal reflection and vertical translation).

Answer:

To transform the pink figure (pre - image) to the yellow figure, we can perform two transformations:

1. Reflection over the y - axis: This flips the pink figure across the vertical line (y - axis) so that its horizontal orientation (left - right) is reversed, moving it to the left side of the y - axis (similar to the yellow figure's horizontal position relative to the y - axis).
2. Vertical translation (downward): After reflection, we translate the reflected figure downward (along the vertical direction, which corresponds to the x - axis in the given graph's labeling) by a few units (e.g., 2 units) to match the yellow figure's vertical position.

Alternatively, a 180 - degree rotation around the origin (or a point) could also be considered, but reflection followed by translation is more intuitive for the L - shaped figures' orientation and position.