Question

Please Help me with this I don’t understand

Polygon E’F’G’H’

is a dilation image of the polygon

EFGH

What is the scale factor of the dilation?

A.3

B.6

C.12

D.1/3

Answer 1

The scale factor of the dilation is 3 ⇒ A

Explanation:

• If a polygon dilated by a scale factor k, then the ratio between its sides and the corresponding sides of its image equals k

• The length of a vertical segment is the difference between the y-coordinates of its endpoints

In the given figure

∵ EFGH is a polygon

∵ E = (-2, 1), H = (-2, -1)

∵ EH is a vertical side

→ By using the 2nd rule above

∴ The length of EH = 1 - (-1) = 1 + 1

∴ The length of EH = 2

∵ E'F'G'H' is its image after dilation by scale factor k

∵ E' = (-2, 5), and H' = (-2, -1)

∵ E'H' is a vertical side

∴ The length of E'H' = 5 - (-1) = 5 + 1

∴ The length of E'H' = 6

→ By using the 1st rule above

∴
`(E'H')/(EH)` =
`(E'F')/(EF)` =
`(H'G')/(HG)` =
`(F'G')/(FG)` = k

∵
`(E'H')/(EH)` = k

∵
`(E'H')/(EH)` =
`(6)/(2)`

∴
`(E'H')/(EH)` = 3

∴ k = 3

∴ The scale factor of the dilation is 3