(Image shown below this of the shape) 3. Consider this dilation Complete sentences

(a) is the image of the dilation a reduction or an enlargement of the original figure? Explain
(b) What is the scale factor? Explain
Answer

a) A reduction

b) The scale factor is 1/2

Step-by-step explanation:

The vertices of the original figure, ABCD are;

A(-2, 4), B(4, 4), C(2, -2), and D(-4, -2)

The vertices of the image, A'B'C'D' are;

A'(-1, 2), B'(2, 2), C'(1, -1), and D'(-2, -1)

a) The length of the side AB = 4 - (-2) = 6 (Distance between points having the same 'x' or 'y' coordinates

The length of the side A'B' = 2 - (-1) = 3

The length of AB = 6 is larger than the length of A'B' = 3, therefore the image A'B'C'D' is a reduction of (is smaller) the figure ABCD

b) The scale factor = The ratio of the lengths corresponding sides of the image to the original figure;

∴ The scale factor =A'B'/AB = A'D'/AD = B'C'/BC = D'C'/DC

AD = √((-4 - (-2))² + (-2 - 4)²) = 2·√10

A'D' = √((-2 - (-1))² + (-1 - 2)²)  = √10

A'D'/AD= √10/(2·√10) = 1/2

Therefore, given that the coordinates of the preimage are 2 × the coordinates of the image, we have;

The scale factor = A'B'/AB = B'C'/BC = D'C'/DC = A'D'/AD =1/2

The scale factor is 1/2, therefore, we multiply the dimensions of the original figure by 1/2 to get the dimensions of the image.

The scale factor = 1/2.

stops on an even number.