Question

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

Answer 1

(I'm using jimthomas5910 coordinates as an example)

Translated: To begin the example of how to draw the transformed figure that is first translated, you’ll want to start by plotting the points as A=(2,3), B=(9,5), and C=(4,-10). That will then form triangle ABC. We are going to translate this triangle into two units to the left. To translate this triangle to where we want it to go, we need to subtract two of every x coordinate, but make sure you keep y coordinate the same. So now we have A’=(0,3), B’=(7,5), and C’=(2,-10). Lastly, plot triangle A’B’C’ and now you have a translated triangle.

Reflected: To reflect a figure it is semi-similar to translating, except to me, a bit simpler. So, let’s use the same points as last time. Start by plotting the points as A=(2,3), B=(9,5), and C=(4,-10). And that forms triangle ABC. To reflect this triangle we take the x coordinate and turn it into its opposite, so A=(2,3) will become A=(-2,3). See how it went from two and three, to negative two and three? So now you can change all the x coordinates to their opposites. So it would be A=(-2,3), B=(-9,5), and C=(-4,-10). Then you can plot those points and now your figure is reflected.

Rotated: I’ve always struggled with rotating figures only because we’re doing a bit more with (x,y) this time, but I think I can explain it well. So, first what you do is, like before, plot your points, and we’re just going to use the original points like before-- A=(2,3), B=(9,5), and C=(4,-10). First thing we’re gonna do is flip the x and y coordinates. So A=(2,3) would become A=(3,2). After that, you change the now, x coordinate to its opposite, so now it would be (-3,2). Now, do that to all points and they become: A=(-3,2), B=(-5,9), and C=(10,4). Once you plot those points you now have a rotated 90 degree triangle.

hope this helped!

Answer 2

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)