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February 5th, 2017, 05:24 AM  #1 
Newbie Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0  triangle, rotate 45 degrees around the centroid
I have a triangle and its center and I need to rotate it 45 degrees around its center in clockwise direction. How can I do it please? The coordinates are A(5,20), B(5,30), C(15,25), centroid is (8.33, 25) Last edited by skipjack; February 5th, 2017 at 08:10 AM. 
February 5th, 2017, 06:53 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239  
February 5th, 2017, 07:24 AM  #3 
Newbie Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0 
Hello. thanks but I need the formula.

February 5th, 2017, 08:01 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239  What do you know about operations with matrices? For a point $(x,y)$ to be rotated about the point $(x_c,y_c)$ by an angle, $\theta$, clockwise, resulting in a rotated image point $(x',y')$ ... $\begin{bmatrix} x'\\ y' \end{bmatrix}= \begin{bmatrix} \cos{\theta} &\sin{\theta} \\ \sin{\theta}&\cos{\theta} \end{bmatrix} \cdot \begin{bmatrix} xx_c\\ yy_c \end{bmatrix}+ \begin{bmatrix} x_c\\ y_c \end{bmatrix}$ 
February 5th, 2017, 09:52 AM  #6 
Newbie Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0 
I don't know operations with matrices, can you do one and i can continue please?

February 5th, 2017, 10:01 AM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239 
$\begin{bmatrix} x'\\ y' \end{bmatrix}= \begin{bmatrix} \cos{\theta} &\sin{\theta} \\ \sin{\theta}&\cos{\theta} \end{bmatrix} \cdot \begin{bmatrix} xx_c\\ yy_c \end{bmatrix}+ \begin{bmatrix} x_c\\ y_c \end{bmatrix}$ the above matrix translates into two equations ... $x' = \cos{\theta}(xx_c) + \sin{\theta}(y  y_c) + x_c$ $y' = \sin{\theta}(xx_c) + \cos{\theta}(y  y_c) + y_c$ using the point $(x,y) = (5,20)$ and $(x_c,y_c) = (8.33,25)$ in the first equation to find the rotated xvalue, $x'$ ... $x' = \cos(45^\circ)(58.33) + \sin(45^\circ)(20  25) + 8.33$ get out your calculator ... what do you get for $x'$ ? 
February 5th, 2017, 10:17 AM  #8 
Newbie Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0 
x′ = 2.45. thanks very much.

February 5th, 2017, 10:21 AM  #9 
Math Team Joined: Jul 2011 From: Texas Posts: 2,516 Thanks: 1239  

Tags 
centroid, degrees, rotate, triangle 
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