Answer:
The scale factor SF = [tex]\frac{7}{3}[/tex] ⇒ C
Step-by-step explanation:
If the point (x, y) dilated by a scale factor n, then the coordinates of its image are (n x, n y)
Let us solve the question
∵ The coordinates of the point K are (-3, 6)
∴ x = -3 and y = 6
∵ The coordinates of its image k' are (-7, 14)
→ From the rule above the image is (n x, n y)
∵ The scale factor is n
∴ n x = -7
∴ n y = 14
→ Substitute x by -3
∵ n (-3) = -7
∴ -3n = -7
→ Divide both sides by -3
∵ [tex]\frac{-3n}{-3}[/tex] = [tex]\frac{-7}{-3}[/tex]
∴ n = [tex]\frac{7}{3}[/tex]
→ Substitute y by 6
∵ n (6) = 14
∴ 6n = 14
→ Divide both sides by 6
∵ [tex]\frac{6n}{6}[/tex] = [tex]\frac{14}{6}[/tex]
∴ n = [tex]\frac{7}{3}[/tex]
→ Both coordinates gave the same value of n
∴ The scale factor SF = [tex]\frac{7}{3}[/tex]
