diff --git a/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md b/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md index 766c575..338e10b 100644 --- a/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md +++ b/Grade 10/Math/MPM2DZ/Unit 1: Analytical Geometry.md @@ -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). + + ### 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. + + ### 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.