From 9d9cf5aa04640a98580506c3789f87fbefd8096c Mon Sep 17 00:00:00 2001 From: James Su Date: Wed, 18 Sep 2019 14:57:51 +0000 Subject: [PATCH] Update Unit 1: Analytical Geometry.md --- .../MPM2DZ/Unit 1: Analytical Geometry.md | 40 ++++++++++++++++++- 1 file changed, 39 insertions(+), 1 deletion(-) diff --git a/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md b/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md index 279fa68..766c575 100644 --- a/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md +++ b/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md @@ -60,4 +60,42 @@ Let $`x_c, y_c`$ be the center $`(x - x_c)^2 + (y - y_c)^2 = r^2`$ -To get the center, just find a $`x, y`$ such that $`x - x_c = 0`$ and $`y - y_c = 0`$ \ No newline at end of file +To get the center, just find a $`x, y`$ such that $`x - x_c = 0`$ and $`y - y_c = 0`$ + +## Triangle Centers + +## Centroid +The centroid of a triangle is the common intersection of the 3 medians. The centroid is also known as the centre of mass or centre of gravity of an object (where the mass of an object is concentrated). + +### Procedure To Determine The Centroid +1. Find the equation of the two median lines. **The median is the line segment from a vertex from a vertex to the midpoint of the opposite side**. +2. Find the point of intersection using elimnation or substitution. + +- Alternatively, only for checking your work, let the centroid be the point $`(x, y)`$, and the 3 other points be $`(x_1, y_1), (x_2, y_2), (x_3, y_3)`$ respectively, then the +centroid is simply at $`(\dfrac{x_1 + x_2 + x_3}{3}, \dfrac{y_1+y_2+y_3}{3})`$ + +## Circumcentre +The circumcentre ($`O`$) of a triangle is the common intersection of the 3 perpendicular bisectors of the sides of a triangle. + +### Procedure To Determine The Centroid +1. Find the equation of the perpendicular bisectors of two sides. **A perpendicular (right) bisector is perpendicular to a side of the triangle and passes through the midpoint of that side of the triangle**. +2. Find the point of intersection of the two lines using elimination or substitution. + + +## Orthocentre +The orthocenter of a triangle is the common intersection of the 3 lines containing the altitudes. + +### Procedure To Determine The Orthocentre +1.Find the equation of two of the altitude lines. **An altitude is a perpendicular line segment from a vertex to the line of the opposite side.** +2. Find the point of intersection of the two lines using elimination or substitution. + + +## Classifying Shapes + + + + +## Properties Of Quadrilaterals + + +