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 reflecting it across the x-axis and the y-axis, we'll perform the reflections step by step.

1. Reflecting across the x-axis: When we reflect a point \((x, y)\) across the x-axis, the new coordinates become \((x, -y)\). Therefore:

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

   After reflecting across the x-axis, the new coordinates of the vertices are:

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

2. Reflecting across the y-axis: Next, when we reflect a point \((x, y)\) across the y-axis, the new coordinates become \((-x, y)\). We take the coordinates obtained after the x-axis reflection and reflect them across the y-axis:

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

Now, after reflecting across both axis, the final coordinates of the vertices of rectangle A'B'C'D' are:

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

Thus, the final coordinates for the rectangle A'B'C'D' are:

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