Question

Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:

Octagon ABCDEFGH with ordered pairs at A at 3, 1, at B 3, negative 1, C 1, negative 3, D negative 1, negative 3, E negative 3, negative 1, F negative 3, 1, G negative 1, 3, H 1, 3. Octagon A prime B prime C prime D prime E prime F prime G prime H prime with ordered pairs A prime 6, 2, at B prime 6, negative 2, at C prime 2, negative 6, at D prime negative 2, negative 6, at E prime negative 6, negative 2, at F prime negative 6, 2, at G prime negative 2, 6, at H prime 2, 6

If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated?

one half
2
4
one quarter

Answer 1

The correct option is 2. The scale factor of dilation is 2.

Explanation:

It is given that Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H'.

The center of dilation is origin.

Let the scale factor is k.

If a figure dilated with scale factor k and center at origin, then

`(x,y)\rightarrow (kx,ky)`

The coordinate of A are (3,1) and coordinates of A' are (6,2).

Since scale factor is k and center of dilation is origin, therefore

`k=(x')/(x)=(y')/(y)`

`k=(6)/(3)=2`

Therefore scale factor of dilation is 2. Second option is correct.