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

Answer:

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

Step-by-step 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 $\frac{1}{2}$

That is, the size of the rectangle is reduced by the factor $\frac{1}{2}$.

Then, the vertices of the new rectangle will be,

(1,-2) changes to $\frac{1}{2}\times (1,-2)$ = $(\frac{1}{2},-1)$

(1,2) changes to $\frac{1}{2}\times (1,2)$ = $(\frac{1}{2},1)$

(-1,2) changes to $\frac{1}{2}\times (-1,2)$ = $(\frac{-1}{2},1)$

(-1,-2) changes to $\frac{1}{2}\times (-1,-2)$ = $(\frac{-1}{2},-1)$

So, the vertices of the dilated rectangle are $(\frac{1}{2},-1)$, $(\frac{1}{2},1)$, $(\frac{-1}{2},1)$ and $(\frac{-1}{2},-1)$.

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

Answer 2

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