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Update Unit 1: Analytical Geometry.md

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James Su 2019-09-18 15:00:20 +00:00
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Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md
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@ -67,6 +67,8 @@ To get the center, just find a $`x, y`$ such that $`x - x_c = 0`$ and $`y - y_c
## 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).
<img src="http://mathwords.com/c/c_assets/centroid.jpg" width="300">
### 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.
@ -77,14 +79,17 @@ 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.
<img src="http://mathbitsprep.org/Geometry/Constructions/perpbis1ba.jpg" width="300">
### 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.
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Triangle.Orthocenter.svg/1200px-Triangle.Orthocenter.svg.png" width="300">
### 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.