Dilations

How do you determine if a dilation is an enlargement or reduction?

• Compare the scale factor to 1: if >1 it's an enlargement, if <1 it's a reduction.

• If the shape becomes larger, it's an enlargement; if smaller, it's a reduction.

• Dilation always results in an enlargement regardless of the scale factor.

• The dilation is an enlargement if the original shape is a square.

If the scale factor is greater than 1, what type of dilation occurs?

• A reduction occurs when the scale factor is greater than 1.

• An enlargement occurs when the scale factor is greater than 1.

• A reflection occurs when the scale factor is greater than 1.

• A rotation occurs when the scale factor is greater than 1.

If the scale factor is less than 1, what type of dilation occurs?

• A reduction occurs when the scale factor is less than 1.

• An enlargement occurs when the scale factor is less than 1.

• No dilation occurs when the scale factor is less than 1.

• A reflection occurs when the scale factor is less than 1.

What is the image of a triangle ABC after a dilation with a scale factor of 1/2?

• The image will be a smaller triangle, half the size of the original.

• The image will be a larger triangle, double the size of the original.

• The image will remain the same size as the original triangle.

• The image will be a triangle with one angle changed.

If triangle ABC has vertices A(2, 3), B(4, 5), and C(6, 7), what are the coordinates after a dilation with a scale factor of 3?

• A'(6, 9), B'(12, 15), C'(18, 21)

• A'(4, 6), B'(8, 10), C'(12, 14)

• A'(3, 4), B'(6, 8), C'(9, 12)

• A'(9, 12), B'(15, 18), C'(21, 24)

How do you find the coordinates of a dilated point using a scale factor?

• Add the original coordinates to the scale factor.

• Subtract the scale factor from the original coordinates.

• Multiply the original coordinates by the scale factor.

• Divide the original coordinates by the scale factor.

True or False: A dilation can change the shape of a figure.

• True

• False

• Only in certain cases

• Depends on the type of figure

What is the relationship between the original figure and its image after dilation?

• The original figure and its image are congruent, meaning they have the same size and shape.

• The original figure and its image are similar, meaning they have the same shape but different sizes.

• The original figure and its image are identical, meaning they are exactly the same.

• The original figure and its image are unrelated, meaning they have no similarities.

What is the rule for dilating a point (x, y) by a scale factor of 1/2?

• (x, y) → (1/2 x, 1/2 y)

• (x, y) → (2x, 2y)

• (x, y) → (x/2, y/2)

• (x, y) → (x + 1, y + 1)

What happens to the area of a figure when it is dilated by a scale factor of k?

• The area remains the same.

• The area is multiplied by k.

• The area is multiplied by k².

• The area is divided by k.