Mathematics, 17.01.2020 09:31 fredvales19

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 a'b'c'. wh

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Answer from: sophiebeardsley94

we have that

$A(0,2)\ B(2,2)\ C(2,0)\\A'(-4,-1)\ B'(1,-1)\ C'(1,-6)$

we know that

Triangles ABC and A'B'C' are similar

Step

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

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

a) distance AB

$dAB=\sqrt{(2-2)^{2}+(2-0)^{2}}$

$dAB=\sqrt{(0)^{2}+(2)^{2}}$

$dAB=2\ units$

b) distance A'B'

$dA'B'=\sqrt{(-1+1)^{2}+(1+4)^{2}}$

$dA'B'=\sqrt{(0)^{2}+(5)^{2}}$

$dA'B'=\sqrt{25}\ units$

$dA'B'=5\ units$

Step

Find the scale factor

$scale\ factor= \frac{measure\ A'B'}{measure\ AB} \\ \\ scale\ factor=\frac{5}{2} \\ \\ scale\ factor=2.5$

therefore

the answer is

the scale factor of the dilation is equal to 2.5

Answer from: rfcordray307

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:

$\sqrt{(c-a)^2+(d-b)^2}$

a) length AB

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

$\sqrt{(2-0)^2+(2-2)^2} =\sqrt{4}=2 units$

b) length A'B'

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

$\sqrt{(1-(-4))^2+(-1-(-1))^2}=\sqrt{(1+4)^2+0}=\sqrt{5^2}=5 units$

Now we Find the scale factor of the dilation?

Scale factor is:

$\dfrac{Length A'B'}{Length AB}\\\\\\=\dfrac{5}{2}\\\\=2.5$

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

Answer from: Quest

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

Answer from: Quest

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