Question

A.ΔS'T'U' is a 90° rotation about the origin of ΔSTU.B.ΔS'T'U' is a 180° rotation about the origin of ΔSTU.C.ΔS'T'U' is a 270° rotation about the origin of ΔSTU.D.ΔS'T'U' is a 360° rotation about the origin of ΔSTU.

Answer 1

By definition, a Rotation is a transformation in which a figures is turned about a Center of rotation.

It is important to remember that, in transformations, the Image is the figure obtained after the transformation and the Pre-Image is the original figure.

In this case, you can identify that the vertices of the Pre-Image STU have the following coordinates:

$\begin{gathered} S(-4,2) \\ T(-1,3) \\ U(-2,1) \end{gathered}$

And the coordinates of the vertices of its Image, are:

$\begin{gathered} S^{\prime}(4,-2) \\ T^{\prime}(1,-3) \\ U^{\prime}(2,-1) \end{gathered}$

Notice that the coordinates of the Image are obtained by multiplying the coordinates of the Pre-Image by -1.

By definition, when you rotate a figure 180° about the Origin, the rule is:

$\mleft(x,y\mright)\to(-x,-y)$

Therefore, the answer is: Option B.