Question

Hello, I have tried this practice problem so many times and watched so many math videos and still I am only getting .13 correct. See question attached. Thank you

Answer 1

To solve this problem the first thing we have to do is to find the coordinates of the original points:

$\begin{gathered} F(1,-2) \\ G(3,1) \\ H(5,-2) \\ J(3,-5) \end{gathered}$

Now that we have the original points we have to remember that a rotation of 90 degrees clockwise is given by:

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

This means that we have to interchange the coordinates and then change the sign of the second one. With this in mind we have:

$\begin{gathered} F^{\prime}(-2,-1) \\ G^{\prime}(1,-3) \\ H^{\prime}(-2,-5) \\ J^{\prime}(-5,-3) \end{gathered}$

Now we need to translate the coordinates two units up, to do this we have to remember that a general translation is given by:

$(x,y)\rightarrow(x+a,y+b)$

In this case we are only shifting in the y direction, then a=0; furthermore we know that we have to shift the figure two units up this means that b=2. Then in this case we have the translation:

$(x,y)\rightarrow(x,y+2)$

Therefore our final coordinates are:

$\begin{gathered} F^{\prime}^{\prime}(-2,1) \\ G^{\prime}^{\prime}(1,-1) \\ H^{\prime}^{\prime}(-2,-3) \\ J^{\prime}^{\prime}(-5,-1) \end{gathered}$