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Line segment AB has vertices A(-3,4) and B(1,-2). A dilation, centered at the origin, is applied to AB. The image has vertices A’ (-1,4/3) and B’ (1/3,-2/3). What is the scale factor of the dilation?

1/6
1/3
3
6
(On the 2/3 fraction the negative sign is only by the 2)

1 Answer

2 votes

Answer:

The scale factor is
(1)/(3)

Explanation:

The given line segment AB has vertices A(-3,4) and B(1,-2).

The image has vertices
A'(-1,(4)/(3)) and
B'((1)/(3),(-2)/(3)).

The mapping for a dilation with scale factor
k centered at the origin is


(x,y)\to (kx,ky)

Let the scale factor for the dilation be
k.

Then,


A(-3,4)\to A'(-3k,4k)

Comparing
A'(-3k,4k) to
A'(-1,(4)/(3)), we have


-3k=-1


\Rightarrow k=(1)/(3)

Or


4k=(4)/(3)


\Rightarrow k=(4)/(3)* (1)/(4).


\Rightarrow k=(1)/(3).

We could have also used the second point to obtain the same result.

User Sycx
by
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