Question

writing a rule for a rotation
triangle abc was rotated about the origin. which rule describes the rotation?
$r_{0,180^{circ}}$
$r_{0,90^{circ}}$
$r_{0,270^{circ}}$
$r_{0,360^{circ}}$

Explanation:

Step1: Recall rotation rules

In a 2 - D coordinate system, a rotation of $180^{\circ}$ about the origin $(0,0)$ changes the sign of both the $x$ and $y$ - coordinates of a point $(x,y)$ to $(-x,-y)$. A $90^{\circ}$ rotation changes $(x,y)$ to $(-y,x)$, a $270^{\circ}$ rotation changes $(x,y)$ to $(y, - x)$ and a $360^{\circ}$ rotation leaves the point unchanged.

Step2: Observe the transformation

By looking at the pre - image $\triangle ABC$ and the image $\triangle A'B'C'$, we can see that the orientation of the triangle has been flipped completely. For example, if we consider a point on $\triangle ABC$ and its corresponding point on $\triangle A'B'C'$, the $x$ and $y$ coordinates have their signs reversed. This is characteristic of a $180^{\circ}$ rotation about the origin.

Answer:

$R_{0,180^{\circ}}$