Update Unit 1: Analytical Geometry.md

Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md

@@ -104,3 +104,11 @@ The orthocenter of a triangle is the common intersection of the 3 lines containi
 
 <img src="https://files.catbox.moe/asixh9.png" width="500">
 
+## Ratios
+- To calculate each segment of the line given the ratio, the answer is simply 
+- $`(x_1 + \dfrac{x_2 - x_1}{r}, y_1 + \dfrac{y_2 - y1}{r})`$, where $`r, (x_1,y_1) (x_2,y_2)`$ are the  **total** ratio, first point and second point respectively.
+- Note that the above is for moving up a line. When moving down, we simply subtract like so:
+- $`(x_2 - \dfrac{x_2 - x_1}{r}, y_2 - \dfrac{y_2 - y1}{r})`$
+- For example, from a point like $`(2, 3)`$ to a point ($`5, 6)`$, and having a ratio of $`2:1`$ split at point $`P`$, the coordindates of point $`P`$ is simply 
+- $`(5 - \dfrac{5-2}{3}, 7 - \dfrac{6-3}{3})`$
+- Which is $`(4, 6)`$