Question

if the red triangle is rotated 180 degrees, then reflected over y = 2 what is the final image? green triangle blue triangle orange triangle red triangle

Explanation:

Step1: 180 - degree rotation rule

For a 180 - degree rotation about the origin of a point $(x,y)$ in the coordinate - plane, the new point is $(-x,-y)$. After rotating the red triangle 180 degrees, the positions of its vertices change according to this rule.

Step2: Reflection over $y = 2$ rule

The formula for reflecting a point $(x,y)$ over the line $y = k$ is $(x,2k - y)$. Here $k = 2$, so the new $y$ - coordinate of a point $(x,y)$ after reflection over $y = 2$ is $4 - y$. After performing this reflection on the rotated triangle, we can determine the final image.

Answer:

(No specific answer can be given as there is no information about the positions of the green, blue, orange triangles. But the above are the steps to find the final image of the red - triangle transformation.)