Use the image to answer the question.

Question

image of a quadrilateral labeled D with side lengths of 6, 8, 6, 8 and a second quadrilateral labeled D prime with side lengths of 21, 28, 21, 28

Determine the type of dilation shown and the scale factor used.
Reduction with scale factor of 2.6
Reduction with scale factor of 3.5
Enlargement with scale factor of 2.6
Enlargement with scale factor of 3.5

Answer 1

To determine the type of dilation and the scale factor, we need to compare the side lengths of both quadrilaterals D and D'.

Quadrilateral D has side lengths of:

• 6
• 8
• 6
• 8

Quadrilateral D' has side lengths of:

• 21
• 28
• 21
• 28

Now we calculate the scale factor by comparing the corresponding sides:

For the sides labeled 6 in D and 21 in D': Scale factor = Length in D' / Length in D = 21 / 6 = 3.5

For the sides labeled 8 in D and 28 in D': Scale factor = Length in D' / Length in D = 28 / 8 = 3.5

Since the side lengths of D' are greater than those of D, this represents an enlargement.

Thus, the type of dilation shown is Enlargement with a scale factor of 3.5.