Rotating a triangle

[JoJo999]

Given triangle LMN with vertices (-5,2), M(-2,4) and N(0,1) what will the new vertices be if the triangle is rotated 180^o clockwise about Point L.

Please help, I have no idea how to even start. I think L is (5,2) but what about M and N?

 

[JoJo999]

Triangle LMN

Can you please help--comments aside. Thanks

I tried using the rules for rotation about the origin--obviously it is not rotated about the origin but about L right? then I thought well, maybe once you get point L 180^o M and N would be a simple transformation. So I tried using the formula (-5+h, 2+K) = (5,2) H=10 K=0 and applied it to M and N and got (8,4) and
(10, 1) I don't think any of it is right.

Would you so kindly guide me???

 

[pka]

Given triangle LMN with vertices (-5,2), M(-2,4) and N(0,1) what will the new vertices be if the triangle is rotated 180^o clockwise about Point L. I think L is (5,2) but what about M and N?

You are correct about point \(\displaystyle L'=L\).
The the points \(\displaystyle M,~L,~\&~M'\) are colinear.
\(\displaystyle M~\&~M'\) have \(\displaystyle L\) between them at equal distance.
In fact \(\displaystyle M'=(-8,0)\).
Draw the diagram.
You find \(\displaystyle N'\).

 

[JoJo999]

Triangle LMN

Wait, we are rotating around L so L stays as (=5,2) But how do you know what numbers M' and N' are????
I drew the triangle but I must have a visual problem because I can't get it. Is there a formula that can be used. Please help--I am getting so-0-0 frustrated.

Thanks

 

[pka]

Is there a formula that can be used. Please help--I am getting so-0-0 frustrated.

I gave you the most intuitive way to do this.
To rotate any point \(\displaystyle (x,y)\) about a point \(\displaystyle (h,k)\) through an angle \(\displaystyle \Theta\):
\(\displaystyle \left\{ \begin{array}{l} x' = \left( {x - h} \right)\cos (\Theta ) - \left( {y - k} \right)\sin (\Theta ) + h \\ y' = \left( {x - h} \right)\sin (\Theta ) + \left( {y - k} \right)\cos (\Theta ) + k \\ \end{array} \right.\)

 

[JoJo999]

Triangle LMN

Thanks so much--I was trying to make something difficult out of something simple. :razz: