Answer:
D'G' = 52.5 units
Step-by-step explanation:
Since the dilatation is centred at the origin then multiply the original coordinates by the scale factor 3.5
D' = (1 × 3.5, 7 × 3.5 ) = (3.5, 24.5 )
G' = (- 8 × 3.5, - 5 × 3.5 ) = (- 28, - 17.5 )
Calculate D'G' using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = D' (3.5, 24.5) and (x₂, y₂ ) = G' (- 28, - 17.5)
D'G' = [tex]\sqrt{(-28-3.5)^2+(-17.5-24.5)^2}[/tex]
= [tex]\sqrt{(-31.5)^2+42^2}[/tex]
= [tex]\sqrt{992.25+1764}[/tex]
= [tex]\sqrt{2756.25}[/tex]
= 52.5 units
