Exploring Dilations: Area and Perimeter

The video covers Unit 5, focusing on dilations, transformations that change the size but not the shape of figures. It explains how to calculate scale factors and apply them to various geometric shapes, including triangles and quadrilaterals. The video also discusses the effects of dilations on area and perimeter, providing examples to illustrate these concepts.

What does a dilation in geometry do to a shape?

• Changes its color

• Alters its angles

• Makes it a different shape

• Modifies its size but not its shape

How do you find the scale factor in a dilation?

• Pre-image length plus image length

• Sum of image and pre-image lengths

• Image length divided by pre-image length

• Pre-image length minus image length

What happens to a figure when the scale factor is between 0 and 1?

• It remains unchanged

• It becomes smaller

• It rotates

• It becomes larger

How do you determine the new coordinates of a point after dilation centered at the origin?

• Add the scale factor to each coordinate

• Subtract the scale factor from each coordinate

• Divide each coordinate by the scale factor

• Multiply each coordinate by the scale factor

What is the result of a dilation with a scale factor of 1/3?

• The figure triples in size

• The figure remains the same size

• The figure reduces to one-third of its original size

• The figure increases by one-third of its original size

How is the scale factor determined when comparing two similar figures?

• By dividing the length of a side in the pre-image by its corresponding side in the image

• By adding the lengths of corresponding sides

• By dividing the length of a side in the image by its corresponding side in the pre-image

• By multiplying the lengths of corresponding sides

What is true about the angles of a figure after dilation?

• They become acute

• They remain the same

• They double in size

• They become obtuse

What is the effect of dilation on the perimeter of a figure?

• It is squared

• It is halved

• It is multiplied by the scale factor

• It remains unchanged

How does dilation affect the area of a figure?

• It is multiplied by the scale factor

• It remains unchanged

• It is divided by the scale factor

• It is multiplied by the square of the scale factor

If a rectangle is dilated by a scale factor of 1/3, what happens to its perimeter?

• It becomes one-third

• It triples

• It is multiplied by 1/3

• It remains the same