Question

reflect the figure over the line y = 1. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Recall reflection rule

The distance between a point $(x,y)$ and the line $y = 1$ is $d=y - 1$. After reflection, the new $y$ - coordinate should be at the same distance from $y = 1$ on the other side. So, if the distance is $y - 1$, the new $y$ - coordinate $y'$ satisfies $1-(y')=(y - 1)$, which simplifies to $y'=2 - y$. The $x$ - coordinate remains the same in a reflection over a horizontal line.

Step2: Apply rule to vertices

For each vertex of the triangle, use the transformation $(x,y)\to(x,2 - y)$ to find the coordinates of the reflected vertices. Then plot these reflected vertices to obtain the reflected triangle.

Answer:

To reflect a point $(x,y)$ over the line $y = 1$, the rule is $(x,2 - y)$. For each vertex of the triangle:
Let's assume the vertices of the original triangle are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. The reflected vertices will be $(x_1,2 - y_1),(x_2,2 - y_2),(x_3,2 - y_3)$. Plot these new - found points to get the reflected figure.