# Rotation of points

• December 21st 2010, 08:50 PM
sarahh
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 :(
• December 21st 2010, 09:29 PM
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
• December 21st 2010, 09:41 PM
sarahh
Quote:

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?
• December 21st 2010, 09:59 PM
FernandoRevilla
Quote:

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