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)

The scale factor is

Step-by-step explanation:

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

The image has vertices and .

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

Let the scale factor for the dilation be .

Then,

Comparing to  , we have

Or

.

.

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

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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