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?

Answer 1

the answer would be 2

Explanation:

Answer 2

From the coordinates given we can make out that dilaton is having a scale factor of 2.

Explanaton:

A = (3,1): A' =(6,2)

B = (3,-1) : B' = (6,-2)

C = (1,-3): C' = (2,-6)

D = (-1,-3): D'=(-2,-6)

E =(-3, -1): E'= (-6,-2)

F = (-3,1): F'=(-6,2)

G = (-1,3) : G' = (-2,6)

H = (1,3): H' = (2,-6)

We find that all the coordinates have become doubled as that of original.

Let us find length of AB :

AB = distance between A and B =2 units

A'B' = distance between A' and B' =4 units

i.e. length increased by a scale factor of 2

Hence dilation with scale factor 2.