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?

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MrRoyal MrRoyal · Answer 1 · 2021-10-11T15:07:48+02:00

Dilation involves changing the size of a shape.

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

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)