Question

Triangle JKL has coordinates at J(-1,5), K(1,2), and L(-3,-1). Determine the location of thecoordinates after each transformation.a. Reflection in the x-axis: J'(-1 ,-5), K(5,-2), L'(-3 , 1)b. Translation along the vector <-2,4>: J'(),K'(), L'(1C. 90 degree counterclockwise rotation around the origin:i. J'( ,), K'( ), L'(

Answer 1

The given points of the triangle JKL are:

`\begin{gathered} J(-1,\text{ 5)} \\ K(1,\text{ 2)} \\ L(-3,\text{ -1)} \end{gathered}`

a. Reflection in the x-axis:

The rule for reflection in the x-axis is:

`(x,\text{ y) }\rightarrow\text{ (x,-y)}`

The reflection gives the points:

`\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}`

b. Translation along the vector <-2,4>:

Translation along the vector <-2, 4> gives the point:

`\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}`

C. 90 degree counterclockwise rotation around the origin:

The rule for 90 degrees counterclockwise rotation:

`(x,y)\text{ }\rightarrow\text{ (-y, x)}`

90 degree counterclockwise gives the point:

`\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}`