Dilation and Scale Factors in Geometry

This lesson reviews the use of circular grids in geometry, focusing on the center of dilation and scale factors. It explains how points and images move on a circular grid, using various scale factors to demonstrate dilation. The lesson includes examples with different scale factors, such as two, two and a half, and three and a half, to illustrate how images are scaled. It also covers the dilation of triangles, showing how each point moves based on the scale factor. The lesson concludes with a summary of using circular grids, scale factors, and the center of dilation.

What is the center of dilation in a circular grid?

• The innermost circle

• The midpoint of any line segment

• The center point of the grid

• The outermost circle

If a point is moved double the distance from the center, what is the scale factor?

• 1

• 2

• 3

• 4

How many units does a point move if the scale factor is two and a half?

• 4

• 2

• 5

• 6

What is the scale factor if a point moves three and a half times its original distance?

• 2.5

• 3

• 3.5

• 4

In the context of dilation, what does a scale factor of 3.5 mean?

• The image is enlarged by 3.5 times

• The image is reduced by 3.5 times

• The image is unchanged

• The image is reduced to half its size

When dilating a triangle, how are the points moved?

• Randomly

• Along the same ray from the center

• In a circular motion

• Towards the center

If point A is 3 units from the center and the scale factor is 2, how far is A'?

• 3 units

• 4 units

• 5 units

• 6 units

What happens to point B if it is originally 3 units from the center and the scale factor is 2?

• It moves to 5 units

• It moves to 6 units

• It moves to 4 units

• It moves to 3 units

If point C is 4 units from the center, what is the distance of C' with a scale factor of 2?

• 9 units

• 8 units

• 7 units

• 6 units

How many circles farther out is C' compared to C if the scale factor is 2?

• 1 circle

• 3 circles

• 4 circles

• 2 circles