describe a series of transformations that maps figure 1 to figure 2 to figure 3. be specific.
4.
5.
describe the transformation or sequence of transformations that map each of the preimages to the images listed below.
6. abcd → ghcd
7. mnop → abcd
8. rqop → lmjk
9. gfed → rqop

Question

Accepted Answer

### Problem 4:
# Explanation:
## Step1: Map Figure 1 to Figure 2
To map Figure 1 to Figure 2, we perform a translation (vertical shift) upwards. Let's assume each grid square has a side length of 1 unit. By observing the vertical distance between Figure 1 and Figure 2, we can see that Figure 1 is shifted up by 3 units to get Figure 2. Mathematically, if we consider the coordinates of the vertices of Figure 1, adding 3 to the y - coordinate of each vertex will map it to Figure 2.

## Step2: Map Figure 2 to Figure 3
To map Figure 2 to Figure 3, we perform a translation (horizontal and vertical shift). First, we shift Figure 2 horizontally to the right and vertically upwards. By observing the grid, Figure 2 is shifted right by 5 units and up by 3 units to get Figure 3. So, we add 5 to the x - coordinate and 3 to the y - coordinate of each vertex of Figure 2.

# Answer:
To map Figure 1 to Figure 2: Translate Figure 1 3 units up. To map Figure 2 to Figure 3: Translate Figure 2 5 units right and 3 units up.

### Problem 5:
# Explanation:
## Step1: Map Figure 1 to Figure 4
To map Figure 1 to Figure 4, we perform a reflection over the y - axis. A reflection over the y - axis changes the sign of the x - coordinate of each vertex. If a vertex of Figure 1 has coordinates $(x,y)$, after reflection over the y - axis, it will have coordinates $(-x,y)$.

## Step2: Map Figure 4 to Figure 2
To map Figure 4 to Figure 2, we perform a translation (vertical shift) downwards. By observing the grid, Figure 4 is shifted down by 6 units to get Figure 2. So, we subtract 6 from the y - coordinate of each vertex of Figure 4.

# Answer:
To map Figure 1 to Figure 4: Reflect Figure 1 over the y - axis. To map Figure 4 to Figure 2: Translate Figure 4 6 units down.

### Problem 6: $ABCD
ightarrow GHCD$
# Brief Explanations:
Looking at the figures, $ABCD$ and $GHCD$ share the side $CD$. To map $ABCD$ to $GHCD$, we can perform a reflection over the vertical line passing through $CD$ (or a horizontal reflection depending on the orientation). Alternatively, we can see that it is a reflection (or a translation and reflection combination, but more likely a reflection) such that the part of $ABCD$ with vertices $A$ and $B$ is mapped to $G$ and $H$ while $C$ and $D$ remain fixed (since $CD$ is common). A reflection over the line perpendicular to $AB$ and $GH$ (which is the vertical line through $CD$) will map $A$ to $G$ and $B$ to $H$ while keeping $C$ and $D$ in place.
# Answer:
Reflect $ABCD$ over the vertical line containing $CD$ (or a reflection that maps $A
ightarrow G$ and $B
ightarrow H$ while $C$ and $D$ are invariant) to get $GHCD$.

### Problem 7: $MNOP
ightarrow ABCD$
# Brief Explanations:
First, we can perform a reflection over the vertical line (the axis of symmetry in the diagram) to get a figure that is horizontally aligned with $ABCD$. Then, we perform a translation (horizontal and vertical shift) to map the reflected figure to $ABCD$. Alternatively, we can see that $MNOP$ can be reflected over the vertical line and then translated left and up (or other combinations of reflection and translation) to match the position and orientation of $ABCD$.
# Answer:
Reflect $MNOP$ over the vertical line (the central vertical line in the diagram) and then translate it left and up (or a sequence of reflection and translation) to map to $ABCD$.

### Problem 8: $RQOP
ightarrow LMJK$
# Brief Explanations:
First, we can perform a reflection over the vertical line (the central vertical line) to reverse the horizontal orientation. Then, we perform a translation (downwards and leftwards) to map the reflected figure to $LMJK$. The reflection will change the direction of $RQOP$ and the translation will move it to the position of $LMJK$.
# Answer:
Reflect $RQOP$ over the vertical line (the central vertical line) and then translate it down and left to map to $LMJK$.

### Problem 9: $GFED
ightarrow RQOP$
# Brief Explanations:
First, we can perform a reflection over the vertical line to change the horizontal orientation. Then, we perform a translation (rightwards and up) to map the reflected figure to $RQOP$. The reflection will make the figure have the same horizontal orientation as $RQOP$ and the translation will move it to the correct position.
# Answer:
Reflect $GFED$ over the vertical line (the central vertical line) and then translate it right and up to map to $RQOP$.

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QUESTION IMAGE

Question

Explanation:

Problem 4:

Step1: Map Figure 1 to Figure 2

Step2: Map Figure 2 to Figure 3

Step1: Map Figure 1 to Figure 4

Step2: Map Figure 4 to Figure 2

Answer:

Problem 5: