Respuesta :
Answer:
The answer is "Option C"
Step-by-step explanation:
Given:
point A' and B' are: (0, 6) (6, 9)
To above points we calculate point AB that is (0,2) and (2,3)
Distance formula:
[tex]\bold{D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\\[/tex]
calcuate AB point distance:
[tex]x_1=0\\y_1=2\\x_2=2\\y_2=3[/tex]
[tex]D=\sqrt{(2-0)^2+(3-2)^2}[/tex]
[tex]=\sqrt{2^2+1^2}\\\\=\sqrt{4+1}\\\\=\sqrt{5}\\[/tex]
calculating A'B' point distance:
[tex]x_1=0\\y_1=6\\x_2=6\\y_2=9\\[/tex]
[tex]D=\sqrt{(6-0)^2+(9-6)^2}[/tex]
[tex]= \sqrt{(6)^2+(3)^2}\\\\= \sqrt{36+9}\\\\= \sqrt{45}\\\\= \sqrt{3\times 3\times 5}\\\\= 3\sqrt{5}\\\\[/tex]
If we divide:
[tex]=\frac{3\sqrt{5}}{\sqrt{5}}\\\\=3[/tex]
The final answer is "3".
