Question

what happens to the shape in a dilation

1. scale factor 3 \twhat will happen to the area
2. scale factor 9 \twhat will happen to perimeter
3. scale factor 4 \twhat will happen to the area
4. scale factor 8 \twhat will happen to perimeter
5. scale factor 10 \twhat will happen to perimeter
6. scale factor 2 \twhat will happen to the area
7. scale factor 6 \twhat will happen to the area
8. scale factor 7 \twhat will happen to perimeter
9. scale factor 6 \twhat will happen to perimeter
10. scale factor 7 \twhat will happen to the area
11. scale factor 12 \twhat will happen to perimeter
12. scale factor 6 \twhat will happen to the area
13. scale factor 5 \twhat will happen to perimeter
14. scale factor 6 \twhat will happen to the area

Answer:

To solve problems about the effect of a scale factor on the perimeter and area of a shape during dilation, we use the following rules:

Key Concepts:

• Perimeter: If a shape is dilated by a scale factor \( k \), the perimeter of the dilated shape is \( k \) times the perimeter of the original shape. So, the perimeter changes (scales by \( k \)) when \( k

eq 1 \).

• Area: If a shape is dilated by a scale factor \( k \), the area of the dilated shape is \( k^2 \) times the area of the original shape. So, the area changes (scales by \( k^2 \)) when \( k

eq 1 \).

Solving Each Problem:

1. Scale Factor 3, Area:

The area scales by \( 3^2 = 9 \). So, the area will increase (change) by a factor of 9.

1. Scale Factor 9, Perimeter:

The perimeter scales by \( 9 \). So, the perimeter will increase (change) by a factor of 9.

1. Scale Factor 4, Area:

The area scales by \( 4^2 = 16 \). So, the area will increase (change) by a factor of 16.

1. Scale Factor 8, Perimeter:

The perimeter scales by \( 8 \). So, the perimeter will increase (change) by a factor of 8.

1. Scale Factor 10, Perimeter:

The perimeter scales by \( 10 \). So, the perimeter will increase (change) by a factor of 10.

1. Scale Factor 2, Area:

The area scales by \( 2^2 = 4 \). So, the area will increase (change) by a factor of 4.

1. Scale Factor 6, Area:

The area scales by \( 6^2 = 36 \). So, the area will increase (change) by a factor of 36.

1. Scale Factor 7, Perimeter:

The perimeter scales by \( 7 \). So, the perimeter will increase (change) by a factor of 7.

1. Scale Factor 6, Perimeter:

The perimeter scales by \( 6 \). So, the perimeter will increase (change) by a factor of 6.

1. Scale Factor 7, Area:

The area scales by \( 7^2 = 49 \). So, the area will increase (change) by a factor of 49.

1. Scale Factor 12, Perimeter:

The perimeter scales by \( 12 \). So, the perimeter will increase (change) by a factor of 12.

1. Scale Factor 6, Area:

The area scales by \( 6^2 = 36 \). So, the area will increase (change) by a factor of 36.

1. Scale Factor 5, Perimeter:

The perimeter scales by \( 5 \). So, the perimeter will increase (change) by a factor of 5.

1. Scale Factor 6, Area:

The area scales by \( 6^2 = 36 \). So, the area will increase (change) by a factor of 36.

Summary of Answers:

Problem	Scale Factor	Attribute (Perimeter/Area)	Effect (Change/Scale Factor)
2	9	Perimeter	Changes (scales by \( 9 \))
3	4	Area	Changes (scales by \( 16 \))
4	8	Perimeter	Changes (scales by \( 8 \))
5	10	Perimeter	Changes (scales by \( 10 \))
6	2	Area	Changes (scales by \( 4 \))
7	6	Area	Changes (scales by \( 36 \))
8	7	Perimeter	Changes (scales by \( 7 \))
9	6	Perimeter	Changes (scales by \( 6 \))
10	7	Area	Changes (scales by \( 49 \))
11	12	Perimeter	Changes (scales by \( 12 \))
13	6	Area	Changes (scales by \( 36 \))
14	5	Perimeter	Changes (scales by \( 5 \))
15	6	Area	Changes (scales by \( 36 \))

(Note: For all these problems, since the scale factor \( k
eq 1 \), both perimeter and area change (scale by \( k \) for perimeter, \( k^2 \) for area).)