Answered

a. Draw the dilation of
triangle ABC, with
center (0,0), and scale
factor 2. Label this
triangle A'B'C'
5 뒤
С.
2
b. Draw the dilation of
triangle ABC, with
center (0,0), and scale
factor . Label this
triangle A"B"C".
-7 -6 -5 -4 -B
- 1
4
5
6
B
А
3
C. IS A"B"C" a dilation
of triangle A'B'C'? If
yes, what are the
center of dilation and
the scale factor?

a. Draw the dilation of triangle ABC, with center (0,0), and scale factor 2. Label this triangle A'B'C' 5 뒤 С. 2 b. Draw the dilation of triangle ABC, with cent class=

Answer :

MrRoyal

Dilation involves changing the size of a shape.

  • See attachment for the graphs of ABC, A'B'C and A"B"C"
  • A"B"C" is a dilation of A'B'C', with a scale factor of 1/4

From the given diagram, we have:

[tex]\mathbf{A = (4,-2)}[/tex]

[tex]\mathbf{B = (-2,-2)}[/tex]

[tex]\mathbf{C = (-2,2)}[/tex]

(a) Dilate by scale factor 2 with center (0,0)

We simply multiply the coordinates of ABC by 2

So, we have:

[tex]\mathbf{A' = 2 \times (4,-2) = (8,-4)}[/tex]

[tex]\mathbf{B' = 2 \times (-2,-2) = (-4,-4)}[/tex]

[tex]\mathbf{C' = 2 \times (-2,2) = (-4,4)}[/tex]

See attachment for the graph of A'B'C'

(b) Dilate by scale factor 2 with center (0,0)

We simply multiply the coordinates of ABC by 1/2

So, we have:

[tex]\mathbf{A" = \frac 12 \times (4,-2) = (2,-1)}[/tex]

[tex]\mathbf{B" = \frac 12 \times (-2,-2) = (-1,-1)}[/tex]

[tex]\mathbf{C' = \frac 12 \times (-2,2) = (-1,1)}[/tex]

See attachment for the graph of A"B"C'

(c) Is A"B"C" a dilation of A'B'C

Yes, A"B"C" is a dilation of A'B'C

  • ABC is dilated by 2 to get A'B'C
  • ABC is dilated by 1/2 to get A"B"C

So, the scale factor (k) from A'B'C' to A"B"C" is:

[tex]\mathbf{k = \frac{1/2}{2}}[/tex]

[tex]\mathbf{k = \frac 14}[/tex]

The scale factor (k) from A'B'C' to A"B"C" is 1/4

And the center is (0,0)

Read more about dilations at:

https://brainly.com/question/13176891

${teks-lihat-gambar} MrRoyal

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