Question

I need help with this please! This is Geometry :)

Answer 1

16.

Answer:

The coordinates of the image points are;

$\begin{gathered} F^{\prime}(-3,0) \\ G^{\prime}(-3,2) \\ U^{\prime}(1,4) \\ W^{\prime}(1,2) \end{gathered}$

Explanation:

We want to find the coordinates of the image of given shape after 90 degree counterclockwise rotation.

The rule for 90 degree counterclockwise rotation about the origin can be written as;

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

Firstly, let us write out the coordinates of the preimage points;

$\begin{gathered} F=(0,3) \\ G=(2,3) \\ U=(4,-1) \\ W=(2,-1) \end{gathered}$

We can now apply the rule to determine the coordinates of the image points;

$\begin{gathered} (x,y)\rightarrow(-y,x) \\ F(0,3)\rightarrow F^{\prime}(-3,0) \\ G(2,3)\rightarrow G^{\prime}(-3,2) \\ U(4,-1)\rightarrow U^{\prime}(1,4) \\ W(2,-1)\rightarrow W^{\prime}(1,2) \end{gathered}$

Therefore, the coordinates of the image points are;

$\begin{gathered} F^{\prime}(-3,0) \\ G^{\prime}(-3,2) \\ U^{\prime}(1,4) \\ W^{\prime}(1,2) \end{gathered}$