Question

Use the image to answer the question.

Two quadrilaterals upper A ( 1,-5) upper B (5,-2) upper C (8,-2) upper D (7,-4) and upper E (-5,1) upper F (-2,5) upper G (-2,8) upper H (-4,7) are marked in the second and fourth quadrants of a coordinate plane respectively.

What reflections or sequence of reflections transforms figure ABCD into figure EFGH?

(1 point)
Responses

Reflect ABCD first over the line x=0
, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line x is equal to 0, then over the line y is equal to x .

Reflect ABCD first over the line y=0, then over the line y=x.
Reflect cap A cap b cap c cap d first over the line y is equal to 0 , then over the line y is equal to x .

Reflect ABCD first over the line x=0, then over the line y=0.
Reflect cap A cap b cap c cap d first over the line x is equal to 0 , then over the line y is equal to 0 .

Reflect ABCD over the line y=x
Reflect cap A cap b cap c cap d over the line y is equal to x
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Answer 1

To determine the reflections that transform figure ABCD into figure EFGH, let's analyze the coordinates of the points in both figures.

**Coordinates:**
- **ABCD**:
- A(1, -5)
- B(5, -2)
- C(8, -2)
- D(7, -4)

- **EFGH**:
- E(-5, 1)
- F(-2, 5)
- G(-2, 8)
- H(-4, 7)

Now, let's identify the transformations needed.

1. **Reflect over the line x=0 (the y-axis)**:
- This will change the sign of the x-coordinates.
- New Coordinates after reflection:
- A'(-1, -5)
- B'(-5, -2)
- C'(-8, -2)
- D'(-7, -4)

2. **Next, reflect over the line y=0 (the x-axis)**:
- This will change the sign of the y-coordinates.
- New Coordinates after this second reflection:
- A''(-1, 5)
- B''(-5, 2)
- C''(-8, 2)
- D''(-7, 4)

3. **Lastly, reflect over the line y=x**:
- This will swap the x and y coordinates.
- New Coordinates after this reflection:
- A'''(5, -1)
- B'''(2, -5)
- C'''(2, -8)
- D'''(4, -7)

From the first two reflections, we can see that the shape is being moved from one quadrant to another, but to confirm the final position, reflecting over y=x effectively places the points into their corresponding positions in figure EFGH.

Thus, the correct sequence of transformations is:

**Reflect ABCD first over the line y=0, then over the line y=x.**

So, the correct response is:
**Reflect ABCD first over the line y=0, then over the line y=x.**