diff --git a/content/notes/03-2d-transforms.md b/content/notes/03-2d-transforms.md
index 277b6e6fb..77b4cda0c 100644
--- a/content/notes/03-2d-transforms.md
+++ b/content/notes/03-2d-transforms.md
@@ -8,26 +8,35 @@ tags:
 look into how colours work together
 
 Points lines
-- point is 2d location $
-- two points define a link
+- point is 2d location $(u,v)$
+- two points define a line
 - a polyline with k segments is a sequence of k+1 points
 - a polygon is a polyline where the beginning and ened are the same, we often omit the duplicate point
 - points are vectors
 
-> [!INFO] 
+> [!INFO] polygon and polylines will be specifies in the code
+
+> [!INFO] $[u v]^T$ high T indicates vector 
 
 coordingate systems
 - mathematical
 - image based
 - matrix based
+- ![|300](https://i.imgur.com/m6OAA5T.png)
 
+> [!INFO] make sure to check you are using the right coordinate system
 
 transformations
 - translation
+> [!INFO]  value of change (delta) for each coordinate. for a shape, apply the transformation to each point
 - scaling
 - rotation
+	- rotate by an abgle about the origin
+	- rotation from U towards V, not anti/clockwise
+	- $[u',v'] = [cos(0) - sin(0), sin(0) cos(0)][u,v]$
 - inverse
 - combinations
 
+
 homogenous coordinates
 homogenous transforms