deltamath.com
figure h
figure i
(coordinate grid with x from -12 to 12, y from -12 to 11)
answer attempt 1 out of 3
a dropdown followed by a dropdown.
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Question

deltamath.com
figure h
figure i
(coordinate grid with x from -12 to 12, y from -12 to 11)
answer  attempt 1 out of 3
a dropdown followed by a dropdown.
submit answer

Accepted Answer

To determine the transformation from Figure H to Figure I, we analyze the changes in position and orientation:

### Step 1: Identify the first transformation (Translation)
- Observe the horizontal shift: Figure H’s vertices move right (e.g., a vertex at $ x = -8 $ in H moves to $ x = 1 $ in I? Wait, no—let’s check coordinates. Let’s pick a key vertex of Figure H, say the top vertex: $ (-9, 7) $. In Figure I, a corresponding vertex is $ (8, 6) $? Wait, maybe better to check the "bottom" vertex of H: $ (-7, 1) $, and in I: $ (4, -2) $? Wait, no—maybe first, check the horizontal and vertical shifts. Alternatively, notice that Figure H can be translated (moved) horizontally and vertically, then reflected or rotated? Wait, no—let’s check the direction.

Wait, actually, the first transformation is a **translation** (shift) and then a **rotation** or **reflection**? Wait, no—let’s look at the coordinates. Let's list vertices of Figure H (approximate, from grid):

- Top: $ (-9, 7) $
- Middle right: $ (-1, 4) $
- Middle left: $ (-6, 3) $
- Bottom: $ (-7, 1) $

Figure I vertices:

- Top right: $ (8, 6) $
- Middle left: $ (1, 4) $
- Middle right: $ (3, 3) $
- Bottom: $ (4, -2) $

Wait, maybe the first transformation is a **translation** (e.g., shift right by 10 units? $ -9 + 10 = 1 $? No, $ -9 + 17 = 8 $? Wait, maybe better to see the horizontal shift: from $ x $-values of H (negative) to I (positive), so translation right. Then, a rotation? Wait, no—alternatively, the first transformation is a **translation** (movement) and then a **rotation** or **reflection**. Wait, the problem has two dropdowns: "A [first transformation] followed by a [second transformation]".

Common transformations: Translation (shift), Rotation, Reflection, Dilation.

Looking at the figures, Figure H and I have the same shape (congruent), so no dilation. So first, translation (shift) to align, then rotation or reflection.

Wait, let's check the horizontal shift: Figure H is on the left (negative x), Figure I on the right (positive x). So translate right (e.g., 10 units? Let's check a vertex: $ (-9, 7) $ in H, and in I, a vertex at $ (8, 6) $: $ -9 + 17 = 8 $, $ 7 - 1 = 6 $. Maybe translation right 10 and down 1? No, maybe first translation, then rotation.

Alternatively, the first transformation is a **translation** (e.g., right 10 units) and then a **rotation** (e.g., 90 degrees) or **reflection**. Wait, the standard options for such problems are: Translation, Rotation, Reflection, Dilation.

Assuming the first dropdown is "translation" and the second is "rotation" or "reflection". But let's think again.

Wait, the figure H and I: when you translate Figure H to the right (so it’s in the positive x-region) and then rotate it, or reflect. Alternatively, the first transformation is **translation** (shift) and the second is **rotation** (or reflection).

But since the problem is about geometric transformations (subfield: Geometry, under Mathematics), we proceed.

### Step 1: Translation
Figure H is shifted horizontally (right) and vertically (down/up) to align with Figure I’s position.

### Step 2: Rotation (or Reflection)
After translation, the figure is rotated (e.g., 90 degrees) to match the orientation of Figure I.

But since the problem has dropdowns, the typical answers for such problems are:

First dropdown: **Translation** (e.g., "translation" or "shift")
Second dropdown: **Rotation** (or "Reflection", but rotation is more likely here)

However, to confirm, let's visualize: Figure H is on the left, Figure I on the right. Translate H to the right (so its x-coordinates become positive), then rotate it to match the angle of Figure I.

So the first transformation is **Translation** (e.g., "translation") and the second is **Rotation** (e.g., "rotation").

# Answer:
A $\boldsymbol{\text{translation}}$ followed by a $\boldsymbol{\text{rotation}}$ (or "reflection"—but rotation is more probable here).

(Note: If the dropdown options include "translation" and "rotation", those are the answers.)

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QUESTION IMAGE

Question

Explanation:

Step 1: Identify the first transformation (Translation)

Step 1: Translation

Step 2: Rotation (or Reflection)

Answer: