Question

Learning

Square TUVW is dilated by a scale factor of with respect to the origin.
Then, it is translated 8 units down to produce TUVw
104-7
units
Submit
d
What is the area of T'U'V'W'?
square units
543211
W
5
4-
3
121
-2
9
4
40
What is the perimeter of T'U'V'W"?
ich d
5
6
7
-8
S
U
78 10
GATHS Stow &
V
Que

Answer 1

• perimeter: 80
• area: 400

Explanation:

Given square TUVW, you want the perimeter and area of square T'U'V'W' after it has been dilated by a factor of 5/2 and translated by (0, -8).

Perimeter

Counting grid squares, or reading coordinates, we find the length of a side of square TUVW to be 8 units. Then the perimeter is ...

P = 4s = 4·8 = 32 . . . . units

After dilation, the perimeter of the square is the preimage value multiplied by the dilation factor.

perimeter of T'U'V'W' = (5/2)(perimeter of TUVW) = (5/2)(32 units)

perimeter of T'U'V'W' = 80 units.

Area

The area is the square of the side length. The side length of T'U'V'W' is ...

s' = (5/2)(8) = 20 . . . . units

Then the area is

A' = (s')² = (20 units)² = 400 units²

area of T'U'V'W' is 400 units².

__

Additional comment

Translation is a rigid transformation. It does not change the dimensions, so does not change the perimeter or area of the dilated square.