1. Figure and its dilation image are always similar, then
[tex]\dfrac{AB}{A'B'}=\dfrac{BC}{B'C'}.[/tex]
This means that option B is correct.
2. Triangles AXY and ABC are congruent, then
[tex]\dfrac{AX}{AB}=\dfrac{XY}{BC}=\dfrac{AY}{AC}.[/tex]
Now
[tex]\dfrac{120}{240}=\dfrac{150}{BC}=\dfrac{100}{200}.[/tex]
Therefore,
[tex]BC=2\cdot 150=300\ m.[/tex]
Correct option is A.
3. Figure and its dilation image have congruent corresponding angles:
- [tex]m\angle A=m\angle X;[/tex]
- [tex]m\angle B=m\angle Y;[/tex]
- [tex]m\angle C=m\angle Z.[/tex]
Since [tex]m\angle A=50^{\circ}, m\angle B=100^{\circ},[/tex] then [tex]m\angle C=180^{\circ}-50^{\circ}-100^{\circ}=30^{\circ}.[/tex]
Thus, [tex]m\angle Z=30^{\circ}.[/tex]
