Understanding Dilation in Geometry

The video tutorial explains the concept of dilation in geometry, focusing on quadrilateral WXYZ. It describes how the shape is scaled down using the origin as the center of dilation, resulting in a smaller quadrilateral W'X'Y'Z'. The tutorial guides viewers through writing a rule for dilation, which involves mapping original coordinates to new ones using a scaling factor. The scaling factor is determined by comparing corresponding sides and verifying with specific points. The video emphasizes understanding the scaling factor's impact on the shape's size and provides methods to confirm its accuracy.

What is the initial shape mentioned in the video that undergoes dilation?

• Rectangle LMNO

• Circle PQR

• Quadrilateral WXYZ

• Triangle ABC

What is the center of dilation for quadrilateral WXYZ?

• Point W

• Point X

• The origin

• Point Z

What does a rule for dilation typically involve?

• Rotating the shape

• Changing the color of the shape

• Reflecting the shape

• Mapping coordinates to a new shape

How is the scaling factor represented in the rule for dilation?

• As a scaling factor K

• As a reflection line

• As a translation vector

• As a rotation angle

What is one method to determine the scaling factor?

• By checking the color of the shape

• By comparing corresponding side lengths

• By counting the number of sides

• By measuring the area of the shape

What is the length of side WZ in the original quadrilateral?

• 12 units

• 8 units

• 6 units

• 10 units

What is the scaling factor determined from the side lengths?

• 5/6

• 2/3

• 3/4

• 1/2

What are the coordinates of point Z in the original shape?

• (6, 2)

• (-6, -2)

• (-9, -3)

• (9, 3)

What are the coordinates of Z' after dilation?

• (-6, -2)

• (6, 2)

• (-9, -3)

• (9, 3)

What is the final rule for the dilation of quadrilateral WXYZ?

• Multiply coordinates by 1/2

• Multiply coordinates by 3/4

• Multiply coordinates by 2/3

• Multiply coordinates by 5/6