Question

reflect the figure over the line y = -2. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

Step1: Recall reflection rule

For a point $(x,y)$ reflected over the horizontal line $y = k$, the new - point is $(x,2k - y)$. Here $k=-2$.

Step2: Identify original points

Let the original points of the triangle be $(x_1,y_1),(x_2,y_2),(x_3,y_3)$. Suppose the points are $(4,-7),(5,-5),(6,-8)$.

Step3: Apply the reflection formula

For point $(x_1,y_1)=(4,-7)$:
The new $y$ - coordinate is $2\times(-2)-(-7)=-4 + 7 = 3$, and the $x$ - coordinate remains $4$. So the new point is $(4,3)$.
For point $(x_2,y_2)=(5,-5)$:
The new $y$ - coordinate is $2\times(-2)-(-5)=-4 + 5 = 1$, and the $x$ - coordinate remains $5$. So the new point is $(5,1)$.
For point $(x_3,y_3)=(6,-8)$:
The new $y$ - coordinate is $2\times(-2)-(-8)=-4 + 8 = 4$, and the $x$ - coordinate remains $6$. So the new point is $(6,4)$.

Answer:

Plot the points $(4,3),(5,1),(6,4)$ on the graph.