Given:
The vertices of a triangle are R(3, 7), S(-5, -2), and T(3, -5).
To find:
The vertices of the triangle after a reflection over x = -3 and plot the triangle and its image on the graph.
Solution:
If a figure reflected across the line x=a, then
[tex](x,y)\to (-(x-a)+a,y)[/tex]
[tex](x,y)\to (-x+a+a,y)[/tex]
[tex](x,y)\to (2a-x,y)[/tex]
The triangle after a reflection over x = -3. So, the rule of reflection is
[tex](x,y)\to (2(-3)-x,y)[/tex]
[tex](x,y)\to (-6-x,y)[/tex]
The vertices of triangle after reflection are
[tex]R(3,7)\to R'(-6-3,7)[/tex]
[tex]R(3,7)\to R'(-9,7)[/tex]
Similarly,
[tex]S(-5,-2)\to S'(-6-(-5),-2)[/tex]
[tex]S(-5,-2)\to S'(-6+5,-2)[/tex]
[tex]S(-5,-2)\to S'(-1,-2)[/tex]
And,
[tex]T(3,-5)\to T'(-6-3,-5)[/tex]
[tex]T(3,-5)\to T'(-9,-5)[/tex]
Therefore, the vertices of triangle after reflection over x=-3 are R'(-9,7), S'(-1,-2) and T'(-3,-5).
