Question

5) Polygon ABCDE is show on the coordinate plane below. (8.3B)Polygon ABCDE is dilated using a scale factor of 3. Describe the effects of thedilation on the perimeter and area of the new image.A. The perimeter and the area are 3 times biggerB. The perimeter and the area are 9 times bigger.C. The perimeter is 3 times bigger and the area is 9 times bigger.D. The perimeter is 9 times bigger and the area is 3 times bigger

Answer 1

P = AB + BC +CD + DE + EA

If the polygon is dilated using a scale facor of 3, then:

3P = 3AB + 3BC + 3CD + 3DE +3EA

Factor:

3P = 3(AB + BC +CD + DE + EA)

Therefore, The perimeter is 3 times bigger.

Since the area depends on the sides and the sides have been expanded by a factor of 3:

A = k² square units

So:

A = 3³ square units

A = 9 square units

Therefore the area is 9 times bigger