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Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by?

Answer choices:
A. 1/2
B. 2
C. 3
D.4

Segment AB Is Dilated From The Origin To Create Segment A Prime B Prime At A 0 4 And B 4 6 What Scale Factor Was Segment AB Dilated By Answer Choices A 12 B 2 C class=

Sagot :

Given:

Endpoint of segment AB are A(0,2), B(2,3).

Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).

To find:

The scale factor of dilation.

Solution:

If a figure is dilated about the origin with factor k, then

[tex](x,y)\to (kx,ky)[/tex]

Using this rule, we get

[tex]A(0,2)\to A'(k(0),k(2))[/tex]

[tex]A(0,2)\to A'(0,2k)[/tex]

So, the image of A is A'(0,2k).

It is given that image of A is A'(0,4). So,

[tex]A'(0,2k)=A'(0,4)[/tex]

On comparing the y-coordinates from both sides, we get

[tex]2k=4[/tex]

[tex]k=\dfrac{4}{2}[/tex]

[tex]k=2[/tex]

Therefore, the scale factor is 2 and the correct option is B.

MrRoyalidn

Dilation involves changing the size of a line

The scale factor is 2.

From the graph, the coordinates of AB are:

[tex]\mathbf{A = (0,2)}[/tex]

[tex]\mathbf{B = (2,3)}[/tex]

The coordinates of AB are:

[tex]\mathbf{A' = (0,4)}[/tex]

[tex]\mathbf{B' = (4,6)}[/tex]

Divide A' by A or B' by B to calculate the scale ratio (k)

[tex]\mathbf{k = \frac{A'}{A}}[/tex]

So, we have:

[tex]\mathbf{k = \frac{(0,4)}{(0,2)}}[/tex]

Expand

[tex]\mathbf{k = \frac{2(0,2)}{(0,2)}}\\[/tex]

Divide

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

Hence, the scale factor is 2.

Read more about scale factors at:

https://brainly.com/question/16713785

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