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.
My geometric figure is a square with the following coordinates for its vertices: A(0, 0), B(4, 0), C(4, 4), and D(0, 4).
First, I will reflect the square over the x-axis. This means that the y-coordinates of each vertex will change to their opposite values, while the x-coordinates stay the same. After the reflection, the coordinates of the new vertices are:
A'(0, 0), B'(4, 0), C'(4, -4), and D'(0, -4).
Next, I will translate the reflected square to a new location. I will move it 3 units to the right and 2 units down. This means that I will add 3 units to each x-coordinate and subtract 2 units from each y-coordinate. The coordinates of the new vertices after the translation are:
A''(3, -2), B''(7, -2), C''(7, -6), and D''(3, -6).
In the original figure, all angles of the square are right angles. After the reflection, the angles of the reflected square also remain right angles. However, after the translation, the angles of the final square are no longer right angles. This is because translations preserve shape but do not preserve angles.
The sides of the original square were all equal in length, and this property remains the same in the reflected and translated square. The square shape itself is also preserved throughout the transformation.