Question

Rectangle ABCD has vertices A (-1, -2), B ( -1, -8), C (-8, -8), and D ( -8, -2).
the rectangle ABCD is reflected on the x axis and the y-axis. Find the coordinates of the vertices for rectangle A'B'C'D

Answer 1

To find the coordinates of the vertices of rectangle ABCD after it is reflected on the x-axis and then on the y-axis, we will apply the reflection transformations to each vertex of the rectangle.

**Step 1: Reflect over the x-axis.**
When a point \((x, y)\) is reflected over the x-axis, its new coordinates are \((x, -y)\).

Applying this to each vertex:

- A (-1, -2) → A' (-1, 2)
- B (-1, -8) → B' (-1, 8)
- C (-8, -8) → C' (-8, 8)
- D (-8, -2) → D' (-8, 2)

**Step 2: Reflect over the y-axis.**
When a point \((x, y)\) is reflected over the y-axis, its new coordinates are \((-x, y)\).

Now, we apply this transformation to the vertices obtained after the first reflection:

- A' (-1, 2) → A'' (1, 2)
- B' (-1, 8) → B'' (1, 8)
- C' (-8, 8) → C'' (8, 8)
- D' (-8, 2) → D'' (8, 2)

Thus, the coordinates of the vertices for rectangle A''B''C''D'' after reflecting rectangle ABCD over the x-axis and then the y-axis are:

- A'' (1, 2)
- B'' (1, 8)
- C'' (8, 8)
- D'' (8, 2)

So, the final coordinates of the vertices are:

- A'' (1, 2)
- B'' (1, 8)
- C'' (8, 8)
- D'' (8, 2)