Answer:
A'B' = 34 units
Step-by-step explanation:
Since the dilatation is centred at the origin , then multiply the coordinates by 2
A' = (2(0), 2(- 7) = (0, - 14 )
B' = (2(8), 2(8) = (16, 16)
Calculate the length using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A'(0, - 14) and (x₂, y₂ ) = B'(16, 16)
d = [tex]\sqrt{(16-0)^2+(16+14)^2}[/tex]
= [tex]\sqrt{16^2+30^2}[/tex]
= [tex]\sqrt{256+900}[/tex]
= [tex]\sqrt{1156}[/tex]
= 34
