From 9440480cf4eeaaf2bd9d6bacdc804ca1daeb8508 Mon Sep 17 00:00:00 2001 From: James Su Date: Thu, 19 Sep 2019 11:53:54 +0000 Subject: [PATCH] Update Unit 1: Analytical Geometry.md --- Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md b/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md index 338e10b..34bf95d 100644 --- a/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md +++ b/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 +## 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 $`(4, 6)`$