Question

1. perimeter and area after dilation

7a. a triangle is dilated with scale factor 3. how does perimeter change?
a. 3 times larger
b. 6 times larger
c. 9 times larger
d. no change
7b. a square is dilated with scale factor 1/2. how does area change?
a. 1/4 the original
b. 1/2 the original
c. same as original
d. double
7c. a rectangle is enlarged by scale factor 4. perimeter becomes — area becomes —
a. 4 times 16 times
b. 8 times 8 times
c. same / 4 times
d. 16 times / 4 times
7d. a hexagon is reduced with scale factor 1/3. which is true?
a. perimeter = 1/3, area = 1/9
b. perimeter = 1/9, area = 1/3
c. both perimeter and area = 1/9
d. both perimeter and area = 1/3

Explanation:

Step1: Recall dilation rules

When a two - dimensional figure is dilated by a scale factor $k$, the perimeter of the figure changes by a factor of $k$, and the area changes by a factor of $k^{2}$.

Step2: Solve 7a

A triangle is dilated with a scale factor of 3. The perimeter of a figure changes by the scale factor. So the perimeter is 3 times larger. The area changes by the square of the scale factor, so the area is $3^{2}=9$ times larger. The perimeter change: 3 times larger, answer is C.

Step3: Solve 7b

A square is dilated with a scale factor of $\frac{1}{2}$. The area of a figure changes by the square of the scale factor. So the new area is $(\frac{1}{2})^{2}=\frac{1}{4}$ of the original area. Answer is A.

Step4: Solve 7c

A rectangle is enlarged by a scale factor of 4. The perimeter changes by the scale factor and the area changes by the square of the scale factor. The perimeter becomes 4 times larger and the area becomes $4^{2} = 16$ times larger. Answer is A.

Step5: Solve 7d

A hexagon is reduced with a scale factor of $\frac{1}{3}$. The perimeter changes by the scale factor and the area changes by the square of the scale factor. The perimeter is $\frac{1}{3}$ of the original perimeter and the area is $(\frac{1}{3})^{2}=\frac{1}{9}$ of the original area. Answer is A.

Answer:

7a. C. 3 times larger
7b. A. $\frac{1}{4}$ the original
7c. A. 4 times larger, 16 times larger
7d. A. Perimeter = $\frac{1}{3}$, area = $\frac{1}{9}$