Question

Which image is the dilation of the rectangle with the center of the dilation at the origin and a scale factor of 1/2 ?

Answer 1

A To find the Scale Factor divide= a side in the image /the same side in the figure

Answer 2

The 3rd graph represents the dilated image of the rectangle.

Explanation:

We are given the rectangle having vertices,

(1,-2), (1,2), (-1,2) and (-1,-2).

Now, this rectangle is dilated about the origin by the scale factor of
`(1)/(2)`

That is, the size of the rectangle is reduced by the factor
`(1)/(2)`.

Then, the vertices of the new rectangle will be,

(1,-2) changes to
`(1)/(2)* (1,-2)` =
`((1)/(2),-1)`

(1,2) changes to
`(1)/(2)* (1,2)` =
`((1)/(2),1)`

(-1,2) changes to
`(1)/(2)* (-1,2)` =
`((-1)/(2),1)`

(-1,-2) changes to
`(1)/(2)* (-1,-2)` =
`((-1)/(2),-1)`

So, the vertices of the dilated rectangle are
`((1)/(2),-1)`,
`((1)/(2),1)`,
`((-1)/(2),1)` and
`((-1)/(2),-1)`.

Thus, the 3rd graph shown below represents the dilated image of the rectangle.