Understanding Dilations in Geometry

The video tutorial explains the concept of dilation in geometry, focusing on how to calculate the dilation of points with respect to a center and a scale factor. It provides a detailed walkthrough of two example problems, demonstrating the application of the dilation formula. The tutorial emphasizes understanding the relationship between original and dilated points and how to apply the formula to solve geometric problems.

What is the dilation factor used in the first example problem?

• 2.0

• 1.0

• 0.2

• 0.5

In the context of dilation, what is the significance of the point (0,0)?

• It is the point of reflection.

• It is the center of rotation.

• It is the center of dilation.

• It is the endpoint of the line segment.

Which formula is used to calculate the new coordinates after dilation?

• x' = x - y

• x' = x + y

• x' = a + k(x - a)

• x' = kx + y

What is the new x-coordinate of point P(8,4) after dilation with a factor of 0.2?

• 4.0

• 3.2

• 2.4

• 1.6

What is the new y-coordinate of point P(8,4) after dilation with a factor of 0.2?

• 1.6

• 0.8

• 2.4

• 3.2

In the second example, what are the coordinates of point A?

• (1,2)

• (2,1)

• (3,4)

• (4,3)

What is the dilation factor used in the second example problem?

• 0.5

• 1.0

• 2.0

• 0.25

What is the new x-coordinate of point P(12,5) after dilation in the second example?

• 6

• 9

• 12

• 3

What is the new y-coordinate of point P(12,5) after dilation in the second example?

• 3.75

• 2.5

• 5

• 1.25

Which of the following is a correct interpretation of dilation?

• It enlarges or reduces a figure by a scale factor.

• It translates a figure along a vector.

• It rotates a figure around a point.

• It reflects a figure across a line.