Question

What are the new vertices of triangle LMN, shown, if the triangle is reflected across the horizontal line y = 1, also shown?

Answer 1

As according to given triangle the vertices are:

L(-4,2), M(3,4) and N(4,2)

If any point when reflected from the line y=k then the coordinates changed to (x,2k-y)

So:

`\begin{gathered} L\mleft(-4,2\mright)\rightarrow L^(\prime)(-4,\text{ 2(1)-2}\rightarrow L^(\prime)(-4,0) \\ M(3,4)\rightarrow M^(\prime)(3,\text{ 2(1)-4)}\rightarrow M^(\prime)(3,-2) \\ N(4,2)\rightarrow N^(\prime)(4,\text{ 2(1)-2)=N'(4,0)} \end{gathered}`

So the new coordinates of the triangle when reflected from y=1 are L'(-4,0), M(3,-2) and N'(4,0)