Exploring Dilations and Scale Factors

The video tutorial from MathGuide explains the concept of dilation in geometry, focusing on the center of dilation and the dilation factor, denoted as K. It provides two examples: one with a dilation factor of 0.5, resulting in a smaller triangle, and another with a factor of 1.5, resulting in a larger triangle. The tutorial highlights that dilation preserves angles but changes the size of the figure. It also explains that a K value greater than 1 results in enlargement, while a K value between 0 and 1 results in shrinkage.

What is required to perform a dilation on a shape?

• Only a dilation factor

• A ruler and a protractor

• A center of dilation and a dilation factor

• Only a center of dilation

How do you calculate the new position of a point during dilation?

• Add the dilation factor to the original distance

• Multiply the original distance by the dilation factor

• Divide the original distance by the dilation factor

• Subtract the dilation factor from the original distance

How is the center of dilation marked in the examples?

• With a dot labeled 'C'

• With a cross

• With a dot labeled 'D'

• With a square

What happens to a triangle when it is dilated with a factor of 0.5?

• It changes shape

• It becomes twice as large

• It becomes smaller

• It remains the same size

What is the new position of point A when dilated with a factor of 1.5?

• 3 units left and 6 units up from the center

• 2 units left and 4 units up from the center

• 1.5 units left and 3 units up from the center

• 3 units right and 6 units down from the center

What is the effect of a dilation factor greater than 1 on a shape?

• It grows

• It remains unchanged

• It rotates

• It shrinks

What is the result of dilating a triangle with a factor of 1.5?

• The triangle's area doubles

• The triangle becomes 1.5 times larger

• The triangle's angles become obtuse

• The triangle turns into a different shape

What remains unchanged during a dilation?

• The shape's angles

• The shape's color

• The shape's area

• The shape's perimeter

What does a dilation factor of less than 1 but greater than 0 do to a shape?

• It changes the shape's color

• It reduces the size of the shape

• It makes the shape rotate

• It enlarges the shape

What property of the triangle is preserved after dilation?

• Angles

• Color

• Texture

• Side lengths