# Math Help - Rotation of points

1. ## Rotation of points

In the standard $(x, y)$ coordinate plane, the coordinate of D are $(d, k)$ and the coordintate of E are $(e, k)$. 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 $(2e - d, k)$ but I'm not sure to obtain to it

2. $E$ is the middle point of $DF$ i.e, if $F=(x,y)$ then,

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

Fernando Revilla

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

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

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?
$e=\dfrac{x+d}{2}\Leftrightarrow 2e=x+d \Leftrightarrow x=2e-d$

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

Fernando Revilla