Respuesta :
The given points of the triangle JKL are:
[tex]\begin{gathered} J(-1,\text{ 5)} \\ K(1,\text{ 2)} \\ L(-3,\text{ -1)} \end{gathered}[/tex]a. Reflection in the x-axis:
The rule for reflection in the x-axis is:
[tex](x,\text{ y) }\rightarrow\text{ (x,-y)}[/tex]The reflection gives the points:
[tex]\begin{gathered} J(-1,5)\text{ }\rightarrow J^{^{\prime}}(-1,\text{ -5)} \\ K(1,\text{ 2) }\rightarrow\text{ K'(1, -2)} \\ L(-3,\text{ -1) }\rightarrow\text{ L'(-3, 1)} \end{gathered}[/tex]b. Translation along the vector <-2,4>:
Translation along the vector <-2, 4> gives the point:
[tex]\begin{gathered} J(-1,\text{ 5) }\rightarrow\text{ J'(-3, 9)} \\ K(1,2)\text{ }\rightarrow\text{ K'(-1, 6)} \\ L(-3,\text{ -1) }\rightarrow\text{ L'(-5, 3)} \end{gathered}[/tex]C. 90 degree counterclockwise rotation around the origin:
The rule for 90 degrees counterclockwise rotation:
[tex](x,y)\text{ }\rightarrow\text{ (-y, x)}[/tex]90 degree counterclockwise gives the point:
[tex]\begin{gathered} J(-1,\text{ 5) }\rightarrow\text{ J'(-5, -1)} \\ K(1,\text{ 2) }\rightarrow\text{ K'(-2, 1)} \\ L(-3,-1)\text{ }\rightarrow\text{ L'(1, -3)} \end{gathered}[/tex]