Answer:
The scale factor of the dilation is 3 ⇒ A
Step-by-step 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
∴ [tex]\frac{E'H'}{EH}[/tex] = [tex]\frac{E'F'}{EF}[/tex] = [tex]\frac{H'G'}{HG}[/tex] = [tex]\frac{F'G'}{FG}[/tex] = k
∵ [tex]\frac{E'H'}{EH}[/tex] = k
∵ [tex]\frac{E'H'}{EH}[/tex] = [tex]\frac{6}{2}[/tex]
∴ [tex]\frac{E'H'}{EH}[/tex] = 3
∴ k = 3
∴ The scale factor of the dilation is 3
