Question

Question
Use the image to answer the question. WHICH ANSWER IS CORRECT AND WHY

A coordinate plane shows two triangles A B C and A double dash B double dash C double dash. Both the axes range from negative 6 to 6 in unit increments.

Identify the sequence of transformations that will carry ΔA (-5,2) B (-2,4) C (-3,0) →ΔA" (-1,-2) B" (2,-4) C" (1,0). Give your answer in the form of a composition transformation mapping.

(1 point)
Responses

(x,y)→(x+4,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 4 comma negative y right parenthesis

(x,y)→(x,−y−4)
open paren x comma y close paren rightarrow open paren x comma negative y minus 4 close paren

(x,y)→(x−4,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis x minus 4 comma negative y right parenthesis

(x,y)→(x,−y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y plus 4 right parenthesis
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Answer 1

To find the sequence of transformations that map triangle ΔA (-5, 2) B (-2, 4) C (-3, 0) to triangle ΔA" (-1, -2) B" (2, -4) C" (1, 0), we can analyze the movement of the points in the coordinate plane.

### Step 1: Examine the coordinates of the triangles

- Triangle ΔA is defined by the vertices:
- A (-5, 2)
- B (-2, 4)
- C (-3, 0)

- Triangle ΔA" is defined by the vertices:
- A" (-1, -2)
- B" (2, -4)
- C" (1, 0)

### Step 2: Find transformations step-by-step

First, let's see how the x-coordinates change from ΔA to ΔA":
- For A: -5 to -1 → +4
- For B: -2 to 2 → +4
- For C: -3 to 1 → +4

This suggests a **horizontal translation to the right** by 4 units.

Next, we'll examine the y-coordinates:
- For A: 2 to -2 → -4
- For B: 4 to -4 → -8
- For C: 0 to 0 → 0

This indicates a **reflection over the x-axis** (which changes the sign of the y-coordinates) followed by a **downward translation** by 4 units (since 2 becomes -2, and 4 becomes -4 after reflecting which requires the further downward move).

### Step 3: Combine the transformations

1. **Reflect over the x-axis**: (x, y) → (x, -y)
2. **Translate downward by 4 units**: (x, -y) → (x, -y - 4)

Combining these gives:
- (x, y) → (x, -y) followed by (x, -y) → (x, -y - 4) results in:
- (x, y) → (x, -y - 4)

### Conclusion:
The correct transformation that maps ΔA to ΔA" is:
**(x,y) → (x, -y - 4)**

This is the second option in the provided responses.