5-3: Geometry in Motion

Using Translation, Rotation and Reflection, we are going to construct a figure given a triangle.

Given the following triangle

Construct the following figure using translation, rotation, and reflectionuse all three types of motion to complete the programexplain your steps along the way.

Step by Step Instruction

We start with the given triangle


a. The first step would be to rotate the figureto put it in the right position we have to figure out the angle of rotation. Since we want to move it halfway around in a circular motion we rotate the figure 180 degrees. (Highlight the fixed point you want to turn your figure around, from the "Transform" menu select "Mark Center". Then highlight the figure you want to rotate, from the "Transform" menu select "Rotate". Finally type in the angle you want the figure rotated.)

b. Now we can make a reflection of the new figurehere we have to decide which line segment to flip the figure over to achieve the desired outcome. For the outcome you desire you can flip the figure over the top line segment or the bottom line segment. (Highlight the line segment you want to flip the figure over, from the "Transform" menu select "Mark Mirror". Then highlight the figure you want to reflect, from the "Transform" menu select "Reflect".)



c. The last step is to translate our new figureyou have to determine what is called the translation vector (where you want to position the translation both horizontally and vertically from the original figure. Think about it as moving it along the x and y-axis. After exploring, we can see that we need to move it 2.5cm horizontally and 0cm vertically to get our desired outcome. (Highlight the figure to be translated, from the "Transform" menu select "Translate". Under "Translation Vector select Rectangle" then put in your horizontal and vertical distances)

We have successfully constructed the desire figure using all three motions, translation, rotation, and reflection.

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