Coordinate graphing activity demonstrating geometric transformations of a figure.

Let’s go step by step to understand what each transformation does to Figure #1 (the pre-image).

We are given 5 figures:
- Figure #1: Pre-image (original)
- Figure #2: Translated
- Figure #3: Rotated
- Figure #4: Reflected
- Figure #5: Dilated

We need to match each transformed figure to the correct graph based on how it was changed from Figure #1.

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Step 1: Understand Figure #1 (Pre-image)

Figure #1 is a red shape that looks like a stylized face or mask with eyes, nose, mouth, and ears. It’s centered near the origin but slightly above the x-axis. Let’s note key points:

- The top of the head is around y = 6
- The bottom of the chin is around y = -2
- Left ear goes to about x = -4
- Right ear goes to about x = +4
- Eyes are at approximately (-2, 3) and (2, 3)
- Mouth is a U-shape from x=-2 to x=2 at y=-1 to y=-2

This will be our reference.

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Step 2: Figure #2 — Translated

Translation means sliding the shape without rotating or flipping it. Same orientation, just moved.

Look at Figure #2: The shape is identical in orientation to Figure #1, but it’s shifted down and to the right.

In Figure #1, the center of the face is roughly at (0, 2). In Figure #2, the center is now around (3, -3). So this is a translation: right 3 units, down 5 units? Let’s check one point.

Take the left eye in Figure #1: approx (-2, 3)

In Figure #2, the left eye is at approx (1, -2) → that’s +3 in x, -5 in y → yes, consistent.

So Figure #2 is correctly labeled as “Translated” — it’s slid, not turned or flipped.

✔ Matches the description.

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Step 3: Figure #3 — Rotated

Rotation means turning the shape around a point (usually origin).

Look at Figure #3: The shape is turned sideways. The top of the head is now pointing to the right. That suggests a 90° clockwise rotation (or 270° counterclockwise).

Check a point: In Figure #1, top of head is at (0, 6). After 90° clockwise rotation around origin, (x,y) becomes (y, -x). So (0,6) → (6, 0). In Figure #3, the top of the head is indeed near (6, 0). Good.

Another point: Left eye in Figure #1: (-2, 3) → after 90° CW: (3, 2). In Figure #3, the “left eye” (which is now on the bottom side) is at about (3, 2)? Wait — actually, after rotation, the whole face is rotated, so the eye that was on the left is now on the bottom.

Actually, let’s think visually: if you rotate the face 90° clockwise, the top goes to the right, the right side goes to the bottom, etc. Yes — Figure #3 shows exactly that.

✔ Correctly labeled as “Rotated”.

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Step 4: Figure #4 — Reflected

Reflection means flipping over a line — usually x-axis or y-axis.

Look at Figure #4: The shape is upside-down compared to Figure #1. The chin is now at the top, the forehead at the bottom. That suggests reflection over the x-axis.

Rule for reflection over x-axis: (x, y) → (x, -y)

Check: Top of head in Figure #1: (0, 6) → should become (0, -6). In Figure #4, the top of the “chin” (which was bottom) is at (0, 6)? Wait — no.

Wait — in Figure #4, the shape is flipped vertically. The original bottom (chin at y=-2) is now at y=+2? Actually, looking closely:

In Figure #1: Chin is at y ≈ -2

In Figure #4: The same chin part is now at y ≈ +2? But also, the eyes which were at y=3 are now at y=-3? Let’s check coordinates.

Original left eye: (-2, 3) → reflected over x-axis → (-2, -3)

In Figure #4, where is the left eye? It’s at (-2, -3)? Looking at the graph — yes! The eye that was upper-left is now lower-left. And the whole shape is mirrored vertically.

Also, the mouth: originally a U opening downward (from y=-1 to y=-2), now it’s an inverted U opening upward? Wait — no, in reflection over x-axis, the mouth would flip too.

Actually, in Figure #4, the mouth is still a U-shape but now it’s at the top? No — wait, the entire face is flipped upside down. So the chin is now at the top, forehead at bottom. That matches reflection over x-axis.

But let’s confirm with a point: Original bottom center (chin tip): (0, -2) → reflected over x-axis → (0, 2). In Figure #4, the point that was chin is now at (0, 2)? Looking at the graph — yes, the lowest point of the original is now the highest point in Figure #4? Wait no — in Figure #4, the shape extends from y=-6 to y=2? Hmm.

Wait — perhaps I misread. Let me look again.

Actually, in Figure #4, the shape is symmetric to Figure #1 across the x-axis? Not quite — because in Figure #1, the shape is mostly above x-axis, in Figure #4 it’s mostly below? No — Figure #4 has parts above and below.

Wait — better approach: Compare Figure #1 and Figure #4.

In Figure #1: The two square "eyes" are at top-center.

In Figure #4: The two square "eyes" are at bottom-center.

That means it’s flipped vertically → reflection over x-axis.

Yes — and the rule holds: (x,y) → (x,-y)

Example: Point (0,4) in Figure #1 (top of forehead) → should be (0,-4) in Figure #4. Looking at Figure #4, there is a point at (0,-4) that corresponds to the top of the forehead? Actually, in Figure #4, the top of the shape is at y=2? I’m getting confused.

Alternative: Maybe it’s reflected over the origin? Or over y-axis?

Wait — let’s try reflection over y-axis: (x,y) → (-x,y)

Then left eye (-2,3) → (2,3) — same height, swapped sides. But in Figure #4, the eyes are not swapped horizontally — they’re still on left and right, but now lower.

Actually, looking at Figure #4: The shape is identical to Figure #1 but flipped upside down. So every point (x,y) in Figure #1 becomes (x, -y) in Figure #4.

Check: In Figure #1, the bottom of the chin is at (0, -2). In Figure #4, that point should be at (0, 2). Is there a point at (0,2) in Figure #4? Yes — the top of the “chin” area is at (0,2)? Actually, in Figure #4, the shape has a bump at the top center — that’s the chin now.

Similarly, the top of the head in Figure #1 is at (0,6) → should be (0,-6) in Figure #4. In Figure #4, is there a point at (0,-6)? Looking at the graph — yes, the bottom of the shape is at y=-6, and it’s the forehead now.

Perfect. So Figure #4 is reflection over x-axis.

✔ Correctly labeled as “Reflected”.

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Step 5: Figure #5 — Dilated

Dilation means resizing — making bigger or smaller, keeping same shape and orientation, centered at origin.

Look at Figure #5: The shape is much larger than Figure #1. All parts are stretched out.

For example, in Figure #1, the width from left ear to right ear is about 8 units (from x=-4 to x=4).

In Figure #5, left ear is at x=-8, right ear at x=8 → width 16 units → scale factor of 2.

Height: In Figure #1, from y=-2 to y=6 → height 8 units.

In Figure #5, from y=-4 to y=12? Let’s see: bottom of chin at y=-4? Top of head at y=12? That would be height 16 → scale factor 2.

Check a point: Left eye in Figure #1: (-2,3) → dilated by factor 2 from origin: (-4,6)

In Figure #5, is the left eye at (-4,6)? Looking at the graph — yes! The eye is at (-4,6). Similarly, right eye (2,3) → (4,6) — matches.

Mouth: originally from (-2,-1) to (2,-2) roughly → after dilation: (-4,-2) to (4,-4) — in Figure #5, the mouth is wider and deeper — yes.

So Figure #5 is dilated by scale factor 2 from origin.

✔ Correctly labeled as “Dilated”.

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Conclusion:

All labels match the transformations shown in the graphs.

The task says: “Plot the points on the graphs below. Make sure to plot the points on the correct graph!”

But since we’re not plotting — we’re verifying — and all figures are already drawn and labeled correctly, the answer is that the labeling is accurate.

However, the user might be expecting us to say which figure corresponds to which transformation — but they are already labeled.

Perhaps the task is to recognize that each figure is correctly matched.

Since the instruction is to solve the problem, and the problem is to ensure points are plotted on correct graphs — and they are — then the final answer is that everything is correct.

But maybe the student needs to identify which is which — but they are labeled.

Looking back at the image description: It says “Answer Key” and then instructions to plot points. But since we can’t plot, and the figures are already drawn, perhaps the task is complete.

I think the intended answer is to confirm that each transformation is correctly applied and labeled.

So, Final Answer: All figures are correctly labeled according to their transformations.

But to be precise, since the question is implied to verify or complete the matching, and it’s already done, we can state:

Final Answer:
Figure #2 is translated, Figure #3 is rotated, Figure #4 is reflected, Figure #5 is dilated — all correctly shown.

But perhaps the expected output is just to acknowledge correctness.

Since the user said “Solve the problem accurately”, and the problem is to plot points on correct graphs — but they are already plotted — I think the solution is that the provided graphs are correct.

To match the format, I’ll provide a concise final answer.

Final Answer:
The transformations are correctly applied: Figure #2 (translated), Figure #3 (rotated), Figure #4 (reflected), Figure #5 (dilated) all match their descriptions relative to Figure #1.