Dilation and Scale Factor Concepts

The video tutorial covers the concept of dilations in geometry, explaining how figures can be enlarged or reduced with respect to a center of dilation. It includes examples using Desmos to visualize dilations, discusses how to identify dilations versus translations, and explains the role of scale factors. The tutorial provides detailed examples of dilating various shapes, such as triangles, rectangles, and trapezoids, and concludes with a practical application involving the expansion of a wildlife refuge.

What is a dilation in geometry?

• A transformation that changes the size of a figure while keeping its shape.

• A transformation that rotates a figure around a point.

• A transformation that slides a figure without changing its size.

• A transformation that reflects a figure over a line.

In a dilation, what remains unchanged between the original figure and the image?

• The color of the figure

• The size of the figure

• The angles of the figure

• The position of the figure

What happens to a shape when the scale factor is greater than 1?

• The shape becomes smaller.

• The shape disappears.

• The shape remains the same size.

• The shape becomes larger.

How do you calculate the new coordinates of a point after a dilation with respect to the origin?

• Add the scale factor to each coordinate.

• Divide each coordinate by the scale factor.

• Subtract the scale factor from each coordinate.

• Multiply each coordinate by the scale factor.

How do you determine the scale factor of a dilation?

• By multiplying the side lengths of the image and the original figure.

• By dividing the side length of the image by the corresponding side length of the original figure.

• By adding the side lengths of the image and the original figure.

• By subtracting the side length of the original figure from the image.

What is the scale factor if a line segment of 2 units is dilated to 6 units?

• 2

• 3

• 4

• 6

If a triangle's vertices are dilated by a scale factor of 3, what type of dilation is this?

• Translation

• Enlargement

• Reflection

• Reduction

What is the result of dilating a rectangle with a scale factor of 0.5?

• The rectangle becomes smaller.

• The rectangle reflects.

• The rectangle becomes larger.

• The rectangle rotates.

After dilating a trapezoid with a scale factor of 2, what additional transformation is applied in the example?

• Scaling

• Translation

• Rotation

• Reflection

What is the effect on the area of a shape when it is dilated by a scale factor of 1.5?

• The area remains the same.

• The area becomes zero.

• The area decreases.

• The area increases.