Answer:
a) A reduction
b) The scale factor is 1/2
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.