Dilation and Coordinate Transformation

The video tutorial explains the concept of dilation in geometry, focusing on cases where the center of dilation is not at the origin. It covers how to perform dilation with different scale factors, such as two and one half, by counting the distance from the center of dilation to the points and adjusting the distance according to the scale factor. The tutorial emphasizes the importance of using a graph to visualize the dilation process and highlights that there is no simple algorithm when the center is not at the origin.

What happens to the coordinates of a point when the center of dilation is not at the origin?

• They are added to the coordinates of the new center.

• They need to be recalculated based on the new center.

• They are simply multiplied by the scale factor.

• They remain unchanged.

If the center of dilation is at (2, 3) and the scale factor is 2, what is the new coordinate of point A originally at (2, 5)?

• (2, 7)

• (4, 6)

• (4, 10)

• (2, 10)

How do you determine the new position of a point after dilation with a scale factor of 2?

• Multiply the coordinates by 2.

• Double the distance from the center of dilation.

• Subtract the original coordinates from the center.

• Add 2 to each coordinate.

What is the new coordinate of point C originally at (2, -1) after dilation with a center at (2, 3) and a scale factor of 2?

• (2, -3)

• (2, 5)

• (2, -5)

• (2, 1)

If the center of dilation is at (-2, -5) and the scale factor is 1/2, what is the new coordinate of point A originally at (-2, 3)?

• (-2, -1)

• (-2, -0.5)

• (-2, 0)

• (-2, 1.5)

How do you determine the new position of a point after dilation with a scale factor of 1/2?

• Subtract the original coordinates from the center.

• Multiply the coordinates by 1/2.

• Add 1/2 to each coordinate.

• Halve the distance from the center of dilation.

What is the new coordinate of point B originally at (8, -5) after dilation with a center at (-2, -5) and a scale factor of 1/2?

• (6, -5)

• (3, -5)

• (5, -5)

• (4, -5)

What is the new coordinate of point C originally at (-2, 9) after dilation with a center at (-2, -5) and a scale factor of 1/2?

• (-2, 2)

• (-2, 1)

• (-2, 4.5)

• (-2, 0)

What is the key concept to remember when performing dilation with a center not at the origin?

• Always multiply the coordinates by the scale factor.

• Subtract the coordinates of the center from the original coordinates.

• Always add the coordinates of the center to the original coordinates.

• Calculate the distance from the center and adjust by the scale factor.

What is the new coordinate of point B originally at (-2, 3) after dilation with a center at (-2, -5) and a scale factor of 1/2?

• (-2, 1.5)

• (-2, -0.5)

• (-2, 0)

• (-2, -1)