# Thread: Rotation of points

1. ## Rotation of points

In the standard $\displaystyle (x, y)$ coordinate plane, the coordinate of D are $\displaystyle (d, k)$ and the coordintate of E are $\displaystyle (e, k)$. When D is roated 180 degrees about E the result is F. In terms of d, e, and k, what are the coordinates of F?

The answer is $\displaystyle (2e - d, k)$ but I'm not sure to obtain to it 2. $\displaystyle E$ is the middle point of $\displaystyle DF$ i.e, if $\displaystyle F=(x,y)$ then,

$\displaystyle (e,k)=\left(\dfrac{x+d}{2},\dfrac{y+k}{2}\right)$

Fernando Revilla

3. Originally Posted by FernandoRevilla $\displaystyle E$ is the middle point of $\displaystyle DF$ i.e, if $\displaystyle F=(x,y)$ then,

$\displaystyle (e,k)=\left(\dfrac{x+d}{2},\dfrac{y+k}{2}\right)$

Fernando Revilla
Hmm I still don't quite understand how that helps, can you elaborate some more?

4. Originally Posted by sarahh Hmm I still don't quite understand how that helps, can you elaborate some more?
$\displaystyle e=\dfrac{x+d}{2}\Leftrightarrow 2e=x+d \Leftrightarrow x=2e-d$

$\displaystyle k=\dfrac{y+k}{2}\Leftrightarrow 2k=y+k \Leftrightarrow y=k$

Fernando Revilla

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