Understanding Dilations

The video tutorial explains the concept of dilation in geometry, focusing on how to plot the image of a point under dilation with different scale factors. It provides two examples: one with a scale factor of 3 about a point P, and another with a scale factor of 1/3 about the origin. The tutorial demonstrates how to calculate the new position of a point after dilation by multiplying the distance from the center of dilation by the scale factor, maintaining the direction.

What is the main concept of dilation in geometry?

• Translating a point in a straight line

• Reflecting a point across a line

• Rotating a point around another point

• Scaling a point up or down around another point

If point A is 1 unit down and 2 units left from point P, where will it be after a dilation with a scale factor of 3?

• 6 units down and 3 units left

• 1 unit down and 2 units left

• 2 units down and 4 units left

• 3 units down and 6 units left

What happens to a picture when all its points are pushed three times further from a center of dilation?

• The picture expands

• The picture shrinks

• The picture rotates

• The picture remains unchanged

In the second example, what is the scale factor used for the dilation about the origin?

• One

• Three

• One-third

• Two-thirds

How far is point A from the origin after a dilation with a scale factor of one-third if it was originally 6 units down and 3 units right?

• 2 units down and 1 unit right

• 3 units down and 1.5 units right

• 6 units down and 3 units right

• 1 unit down and 2 units right