Answer:
Option (4)
Step-by-step explanation:
Length of segment between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the figure attached,
Distance between A(0, -3) and B(3, 0) = [tex]\sqrt{(3-0)^2+(0+3)^2}[/tex]
AB = [tex]3\sqrt{2}[/tex]
Distance between A'(-3.5, -4.5) and B'(-8, 0)
Length of A'B' = [tex]\sqrt{(-3.5+8)^2+(-4.5-0)^2}[/tex]
A'B' = [tex]4.5\sqrt{2}[/tex]
Scale factor for dilation = [tex]\frac{4.5\sqrt{2}}{3\sqrt{2}}=1.5[/tex]
Therefore series of transformations will be,
A dilation of figure 1 with scale factor of [tex]\frac{3}{2}[/tex] and then a reflection.
Option (4) will be the answer.
