Understanding Dilation in Geometry

The video tutorial explains how to determine the center of dilation for a triangle. It begins by introducing the concept of dilation and the problem setup, followed by calculating the scale factor. The tutorial then describes a method to find the center of dilation by connecting corresponding points and verifying the result. The explanation concludes with a verification of the center of dilation using changes in coordinates.

What is the primary task when given a dilated triangle and its image?

• To determine the perimeter of the triangles

• To calculate the area of the triangles

• To identify the center of dilation

• To find the scale factor

How do you calculate the scale factor in a dilation?

• By dividing the length of a side in the image by the length of the corresponding side in the original

• By adding the lengths of all sides in the image

• By subtracting the length of a side in the original from the length of the corresponding side in the image

• By multiplying the lengths of all sides in the original

If a side in the original triangle is 2 units and its corresponding side in the image is 4 units, what is the scale factor?

• 1

• 2

• 3

• 4

What is a method to find the center of dilation?

• By comparing the perimeters of the triangles

• By measuring the angles of the triangles

• By connecting corresponding points and finding a common line

• By calculating the area of the triangles

How far is the image point from the center of dilation compared to the original point?

• The same distance

• Twice as far

• Half as far

• Three times as far

What is the significance of the direction when connecting corresponding points to find the center of dilation?

• The direction should be perpendicular

• The direction is irrelevant

• The direction should be the same

• The direction should be opposite

How can you verify the center of dilation using coordinates?

• By comparing the coordinates to a fixed point

• By calculating the sum of the coordinates

• By ensuring the coordinates are identical

• By checking if the change in x and y coordinates is proportional

What theorem can be used to confirm the distances in dilation?

• The Cosine Rule

• The Sine Rule

• The Triangle Sum theorem

• The Pythagorean theorem

What should be the relationship between the image and original point distances from the center of dilation?

• The image should be half as far

• The image should be three times as far

• The image should be twice as far

• The image should be the same distance

What is a key takeaway about the center of dilation?

• It is always at the origin

• It lies on the line connecting corresponding points

• It is irrelevant to the dilation process

• It is always outside the triangles