Question

A square is dilated by a scale factor of 4 to produce a new square. Which of the following represents the relationship between the original area of the square and the new area of the square?

A. The area of the new square is 16 times larger than the area of the original square.
B. The area of the new square is 8 times larger than the area of the original square.
C. The area of the new square is 4 times larger than the area of the original square.
D. The area of the new square is 2 times larger than the area of the original square.

Answer 1

I remember dilation and that it makes it bigger but would it be C? That's my first instinct.

Answer 2

dilation is not about bigger or smaller, its about scale. we can dilate by 1/4 or by 1 all the same

Answer 3

since this is about area, just work the area of a square with sides: n

Answer 4

Okay, so if it's by a scale factor of 4 then is it 4 times larger?

Answer 5

area is affected greater than the linear parts by sclaing

Answer 6

on a coordinate plane...the points of the shape are multiplied by the scale of dilation to create the new figure

Answer 7

a square of side length n has an area of n^2

a square of side length 4n has an area of (4n)^2, or 16n^2

Answer 8

I'm so confused!

Answer 9

we have the area ratio: n^2 to 16n^2 as a result of the dilation

Answer 10

So is it 16 times larger?

Answer 11

i would say it is :)

let n be any number; then the ratio is still 16 times greater

Answer 12

you got it !
using @amistre64 's model it is true that it is 16 times larger

Answer 13

Thank you guys!!

Answer 14

youre welcome, and good luck