27.2k views
3 votes
(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

(Image shown below this of the shape) 3. Consider this dilation Complete sentences-example-1
User Makdu
by
7.5k points

1 Answer

6 votes

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.

User Jamiedanq
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories