Question

A. Draw the dilation of

Answer 1

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:

$\mathbf{A = (4,-2)}$

$\mathbf{B = (-2,-2)}$

$\mathbf{C = (-2,2)}$

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

We simply multiply the coordinates of ABC by 2

So, we have:

$\mathbf{A' = 2 \times (4,-2) = (8,-4)}$

$\mathbf{B' = 2 \times (-2,-2) = (-4,-4)}$

$\mathbf{C' = 2 \times (-2,2) = (-4,4)}$

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:

$\mathbf{A" = \frac 12 \times (4,-2) = (2,-1)}$

$\mathbf{B" = \frac 12 \times (-2,-2) = (-1,-1)}$

$\mathbf{C' = \frac 12 \times (-2,2) = (-1,1)}$

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:

$\mathbf{k = \frac{1/2}{2}}$

$\mathbf{k = \frac 14}$

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:

brainly.com/question/13176891