2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
Given,
Triangles ABC and A'B'C' are similar
For ABC;- (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, 2)
For A'B'C' ;- (x₁, y₁) = (-4, -1) and (x₂, y₂) = (1, -1)
We have to find the scale factor of the dilation;
Here,
Find the distance AB and distance A'B' with the formula
Distance, d = [tex]\sqrt{(y_{2} -y_{1})^{2} +(x_{2} -x_{1} )^{2} }[/tex]
Then,
a) Distance of AB
d AB = [tex]\sqrt{(2-2)^{2}+(2-0)^{2} }[/tex]
d AB = [tex]\sqrt{0^{2} +2^{2} }[/tex]
d AB = √4
Distance of AB = 2 units
b) Distance of A'B'
d A'B' = [tex]\sqrt{(-1+1)^{2} +(1+4)^{2} }[/tex]
d A'B' = [tex]\sqrt{0^{2} +5^{2} }[/tex]
d A'B' = √25
Distance of A'B' = 5 units
Now,
Scale factor;
Scale factor = Distance of AB / Distance of A'B'
Scale factor = 5/2
Scale factor = 2.5
Therefore,
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
Learn more about scale factor here;
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