Translations and Reflections Practice

Answer 1

Here is a practice problem for translations and reflections:

Consider the point A(3, -2).
1. Translate point A -5 units to the right and 3 units up.
2. Reflect point A over the x-axis.
3. Reflect point A over the line y = 3.

Solution:

1. To translate point A -5 units to the right and 3 units up, add -5 to the x-coordinate and add 3 to the y-coordinate of point A.

New coordinates: A'(-2, 1)

2. To reflect point A over the x-axis, keep the x-coordinate the same and change the sign of the y-coordinate.

New coordinates: A(3, 2)

3. To reflect point A over the line y = 3, calculate the distance between the point and the line, double it, and add it to the y-coordinate to find the new y-coordinate. Keep the x-coordinate the same.

Distance from the line: y = 3 - (-2) = 5
New y-coordinate: 2 + 2(5) = 12

New coordinates: A(3, 12)