Question

Triangle JKL has vertices J (-3, 5), K (-1, 0) and L (8, -4). Which of the following represents the translation of triangle JKL along vector <-4, 7> and its reflection across the x-axis?

Answer 1

EXPLANATION:

We are given a triangle with the vertices as shown below;

$\begin{gathered} J=(-3,5) \\ K=(-1,0) \\ L=(8,-4) \end{gathered}$

To translate along the vector,

$<-4,7>$

We shall apply the following rule;

$(x,y)\Rightarrow(x-4,y+7)$

Therefore, for the points given, a translation along the vector (-4, 7) would be;

$\begin{gathered} J(-3,5)\Rightarrow(-3-4,5+7) \\ J^{\prime}=(-7,12) \end{gathered}$$\begin{gathered} K(-1,0)\Rightarrow(-1-4,0+7) \\ K^{\prime}=(-5,7) \end{gathered}$$\begin{gathered} L(8,-4)\Rightarrow(8-4,-4+7) \\ L^{\prime}=(4,3) \end{gathered}$

Now we have the new points as;

$\begin{gathered} J^{\prime}(-7,12) \\ K^{\prime}(-5,7) \\ L^{\prime}(4,3) \end{gathered}$

Next we shall reflect this shape across the x-axis.The rule for reflecting across the x-axis is given as;

$(x,y)\Rightarrow(x,-y)$

Imagine folding the graph page across the horizontal line (x-axis). That way, the x coordinate would still remain but the y coordinate would flip over from top to bottom or bottom to top.

Therefore, with the new coordinates we've determined, a reflection across the x-axis would become;

$\begin{gathered} J^{\prime}(-7,12)\Rightarrow(-7,-12) \\ J^{\doubleprime}(-7,-12) \end{gathered}$$\begin{gathered} K^{\prime}(-5,7)\Rightarrow(-5,-7) \\ K^{\doubleprime}(-5,-7) \end{gathered}$$\begin{gathered} L^{\prime}(4,3)\Rightarrow(4,-3) \\ L^{\doubleprime}(4,-3) \end{gathered}$

The new coordinates after the translation and the reflection would now be;

ANSWER:

$\begin{gathered} J(-3,5)\rightarrow J^{\prime}(-7,12)\rightarrow J^{\doubleprime}(-7,-12) \\ K(-1,0)\rightarrow K^{\prime}(-5,7)\rightarrow K^{\doubleprime}(-5,-7) \\ L(8,-4)\rightarrow L^{\prime}(4,3)\rightarrow L^{\doubleprime}(4,-3) \end{gathered}$