Provide an example of how to draw transformed figures that are translated, reflected, and rotated.

A coordinate grid is very handy when it comes to drawing geometric shapes such as triangles. Let's create an example triangle ABC with the locations

A = (2,3)

B = (9,5)

C = (4,-10)

Plot those points and connect the dots. That forms triangle ABC. We can translate triangle ABC to any other position we want. Let's say we want to shift it 2 units to the left. That means we subtract 2 from each x coordinate while keeping the y coordinates the same. Therefore

A' = (0, 3)

B' = (7, 5)

C' = (2,-10)

Plot triangle A'B'C' and you should see that this is a shifted copy of triangle ABC.

The rotation rules are a bit more complicated, and it depends where you place the center of rotation; however, it is possible to use coordinate math like done above.

Luckily the reflection rules over the x or y axis are fairly simple. If we reflect over the x axis, then we flip the sign of the y coordinate. Or if we wanted to reflect over the y axis, we flip the sign of the x coordinate.

Example: A' = (0,3) reflects over the x axis to get A'' = (0, -3)