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Triangle ABC was dilated and translated to form similar triangle A'B'C'.



What is the scale factor of the dilation?

Triangle ABC was dilated and translated to form similar triangle ABC What is the scale factor of the dilation class=

Respuesta :

calculista

we have that

[tex] A(0,2)\ B(2,2)\ C(2,0)\\A'(-4,-1)\ B'(1,-1)\ C'(1,-6) [/tex]

we know that

Triangles ABC and A'B'C' are similar

Step [tex] 1 [/tex]

Find the distance AB and distance A'B' with the formula

[tex] d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}} [/tex]

a) distance AB

[tex] dAB=\sqrt{(2-2)^{2}+(2-0)^{2}} [/tex]

[tex] dAB=\sqrt{(0)^{2}+(2)^{2}} [/tex]

[tex] dAB=2\ units [/tex]

b) distance A'B'

[tex] dA'B'=\sqrt{(-1+1)^{2}+(1+4)^{2}} [/tex]

[tex] dA'B'=\sqrt{(0)^{2}+(5)^{2}} [/tex]

[tex] dA'B'=\sqrt{25}\ units [/tex]

[tex] dA'B'=5\ units [/tex]

Step [tex] 2 [/tex]

Find the scale factor

[tex] scale\ factor= \frac{measure\ A'B'}{measure\ AB} \\ \\ scale\ factor=\frac{5}{2} \\ \\ scale\ factor=2.5 [/tex]

therefore

the answer is

the scale factor of the dilation is equal to [tex] 2.5 [/tex]

Answer:

Scale factor of dilation is:

2.5

Step-by-step explanation:

" The scale factor, r, determines how much bigger or smaller the dilation image will be compared to the preimage "

we know that

Triangles ABC and A'B'C' are similar as ΔA'B'C' is formed by dilation of ΔABC with some scale factor.

The coordinates of:

A are (0,2)

B are (2,2)

C are (0,2)

A' are (-4,-1)

B' are (1,-1)

and C' are (1,-6)

Find the length AB and length A'B' with the distance formula

The length of a lie segment is same as a distance between the end points of the line segment.

AB has end points A and B.

The distance between two points A(a,b) and B(c,d) is calculated as:

[tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

a) length AB

i.e. distance between (0,2) and (2,2) is:

[tex]\sqrt{(2-0)^2+(2-2)^2} =\sqrt{4}=2 units[/tex]

b) length A'B'

i.e. distance between A'(-4,-1) and B'(1,-1) is:

[tex]\sqrt{(1-(-4))^2+(-1-(-1))^2}=\sqrt{(1+4)^2+0}=\sqrt{5^2}=5 units[/tex]

Now we Find the scale factor of the dilation?

Scale factor is:

[tex]\dfrac{Length A'B'}{Length AB}\\\\\\=\dfrac{5}{2}\\\\=2.5[/tex]

Hence, the scale factor of the dilation is equal to 2.5

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