Design your own geometric figure. Reflect your figure over either the x
- or y
-axis. Then translate it to a new location. Make sure to describe in what direction you are translating the figure (up/down/left/right) and by how many units. Give the coordinates of the new vertices after the reflection and translation. Which properties of your original figure changed, and which stayed the same? Be sure to explain how the angles of your original figure are related to the angles of your final figure.
I will design a simple geometric figure, a square, and apply the reflection and translation operations to it.
Let's define the vertices of the original square as A(0, 0), B(2, 0), C(2, 2), and D(0, 2).
To reflect the square over the x-axis, we keep the x-coordinates the same but change the sign of the y-coordinates. The new vertices of the reflected square are A'(0, 0), B'(2, 0), C'(2, -2), and D'(0, -2).
Now, let's translate the reflected square. We will move it three units to the right and one unit up.
So, we add 3 to all the x-coordinates and 1 to all the y-coordinates of the reflected square. The new vertices after the translation are A''(3, 1), B''(5, 1), C''(5, -1), and D''(3, -1).
In the original square (ABCD), all angles are right angles (90 degrees). After the reflection and translation operations, the angles in the final figure (A''B''C''D'') will still be right angles. The right angles are preserved during reflection and translation.
The properties of the original figure that changed are the positions and coordinates of the vertices. The original figure was at the origin, while the final figure is located three units to the right and one unit up. Additionally, the y-coordinates of the reflected square flipped in sign. However, the shape of a square with equal sides and equal angles is preserved throughout the operations.