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. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Recall reflection rule

For reflection over $y = k$, if a point is $(x,y)$, the new point is $(x,2k - y)$. Here $k=-1$, so the rule is $(x,-2 - y)$.

Step2: Apply rule to vertices

Take each vertex $(x,y)$ of the original figure and calculate the new vertex $(x,-y - 2)$.

Step3: Plot reflected figure

Use the new - found vertices to plot the reflected figure on the coordinate grid.

Answer:

To reflect a point $(x,y)$ over the line $y = - 1$, we use the following rule:
The $x$-coordinate remains the same, and the new $y$-coordinate is given by $y'=-1-(y + 1)=-y - 2$.
Let's assume the vertices of the original figure are $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4)$.
The reflected vertices will be $(x_1,-y_1 - 2),(x_2,-y_2 - 2),(x_3,-y_3 - 2),(x_4,-y_4 - 2)$.
For example, if we have a point $(x,y)=(-5,-4)$:

• The new $y$-coordinate is $-(-4)-2=4 - 2=2$, and the $x$-coordinate remains $-5$. So the reflected point is $(-5,2)$.

We would repeat this process for all vertices of the given figure and then plot the new - formed reflected figure on the coordinate - plane.