We know that a figure is dilated using a scale factor of -1 and we are asked to say how we can obtain the image without using a dilation. The scale factor is the value of the ratio of the side lengths of the image to the corresponding side lengths of the original figure.
Scale Factor = Side Lengths of the Image/Side Lengths of the Original Figure
Note that in this case the scale factor is less than 0. This tells us that it is not a standard situation, because in general, the scale factor is not less than 0. However, let's take a look at how the coordinates of a figure change when it is dilated by a scale factor k.
(x,y) → (kx, ky)
In our case the scale factor is -1, so the coordinates (x,y) will change to (- x, - y). Notice that we know this kind of transformation.
Rotation in the Coordiante Plane
When a point (x,y) is rotated 180 ^(∘) counterclockwise about the origin, then its coordinates (x,y) change to (- x, - y).
This means that we can get the image of a figure that is dilated using a scale factor of -1 by rotating it 180 ^(∘) counterclockwise about the origin.
