Question

1. rotate 180° around (-1,0) and reflect across the x - axis.

Explanation:

Step1: 180 - degree rotation formula

The formula for rotating a point $(x,y)$ 180 degrees around a center $(a,b)$ is $(2a - x,2b - y)$. Here $a=-1$ and $b = 0$, so the formula becomes $(-2 - x,-y)$. Apply this formula to each vertex of the shape (let the vertices of the original shape be $(x_1,y_1),(x_2,y_2),\cdots$). The new vertices after rotation are $(-2 - x_1,-y_1),(-2 - x_2,-y_2),\cdots$.

Step2: Reflection across x - axis formula

The formula for reflecting a point $(x,y)$ across the x - axis is $(x,-y)$. Apply this formula to the vertices obtained from the rotation. If the vertices after rotation are $(x_{r1},y_{r1}),(x_{r2},y_{r2}),\cdots$, the vertices after reflection are $(x_{r1},-y_{r1}),(x_{r2},-y_{r2}),\cdots$. These new vertices represent the final position of the shape after both transformations.

Answer:

The new - position of the shape after the given transformations. (Note: Without the coordinates of the original points of the shape, we can't give exact new - coordinates. But the general process is shown below.)