Dilations Exploration

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What are the three transformations classified as "Rigid Motion"?

Why are these transformations called Rigid Motion?

Below is a graph of Triangle ABC, then a translation (left 4), then a reflection (across the x-axis), then a rotation (90 degrees counter-clockwise). Verify these are rigid motions by checking that the area and perimeter remain unchanged for each triangle

Today, we'll learn about a fourth transformation called a "Dilation"

Draw Triangle ABC with points A(1,2), B(5,1), and C(4,2). Then draw Triangle DEF with points D(2,4), E(10,2), and F(8,4).

Explain how the two triangles pictured above are alike and how are they not alike.

Write down the coordinates for point A and point D. Do you notice any connection?

Do you see the same connection for the other 2 points? Explain.

Use this picture to answer the questions that follow.

Move the points around in the picture above. What do you notice about the corresponding coordinates?

The Scale Factor is the amount that each point was multiplied by away from the center of dilation.

Draw Triangle A'B'C' after a dilation using a Scale Factor of 3. (that means, find the coordinates for points A,B, and C, then multiply the x and y coordiantes by 3).

Use this picture to answer the questions that follow.

So, we know that when (0,0) is the center of dilation, the coordinate points are multiplied by the same scale factor. Look at Point A and Point A' in the above diagram. What is the scale factor of this dilation?

What pattern do you notice about the corresponding side lengths? Are they multiplied by the same scale factor?

Does the Area increase by the same scale factor?

Move the points around in the picture above. Do your answers above stay the same?

Use this picture to answer the questions that follow.

What is the scale factor of the dilation pictured above?

Where is the center of dilation?

What happens to the corresponding angles when the shape is dilated? Feel free to move the points around to see the pattern.

Do the angles increase by the Scale Factor?

Dilations Exploration

Below is a graph of Triangle ABC, then a translation (left 4), then a reflection (across the x-axis), then a rotation (90 degrees counter-clockwise). Verify these are rigid motions by checking that the area and perimeter remain unchanged for each triangle

Draw Triangle ABC with points A(1,2), B(5,1), and C(4,2). Then draw Triangle DEF with points D(2,4), E(10,2), and F(8,4).

Use this picture to answer the questions that follow.

Draw Triangle A'B'C' after a dilation using a Scale Factor of 3. (that means, find the coordinates for points A,B, and C, then multiply the x and y coordiantes by 3).

Use this picture to answer the questions that follow.

Use this picture to answer the questions that follow.

Information: Dilations Exploration