Grade 10 Academic Mathematics Analytic Geometry Unit Test notes
MPM2D1 MPM2D1
MPM2D1 MPM2D1
Math Analytic Geometry Notes
Midpoint
M=((x1+x2)/(2)),((y1+y2)/(2))
Length
L=√(x2-x1)^2+(y2-y1)^2
Finding Slope, Midpoint, and length formulas
Equations of Circles
X^2+y^2=R^2
Properties of Triangles
Property 1: Each median bisects the area of the triangle
Property 2: In any triangle, the three medians intersect at the same point, centroid
Property 3: the mid segment is half the area and half the length and parallel to the opposite sides
Property 4: Centroid divides line in a 2:1 ratio
Properties of Parallelograms
Property 1: Midpoint of adjacent sides of any quadrilateral forms a parallelogram
Property 2: The opposite sides of any parallelogram are the same length
Property 3: The diagonals of a parallelogram bisects one another
Properties of Trapezoids
Property 1: The line segments of a trapezoid is parallel to the parallel sides
Property 2: The line segments joining the midpoints of the non parallel sides is equal to the mean length of the parallel sides. Top side plus the midsegment side divided by 2 is equal to the length of the non parallel side
Properties of Rhombus
Property 1: All sides are equal in length
Property 2: Opposite sides are parallel but they aren’t perpendicular
Property of Circles
Property 1: Diameters of the circle intersects in the center
Property 2: Right bisectors of a chord passes through the center of the circle
Property 3: Perpendicular bisectors of lines of three points intersect at the center
Property 4: Center of the circle is the POI of the right bisector of the sides of the triangle
Find Shortest Distance from line segment AB to C
- find slope, then y-intercept of the line segment AB
- Find the perpendicular slope of line AB
- Match up coordinates of C to the perpendicular slope in y=mx+b format
- Find POI of line C and AB to see where ^ line intersects with line AB through substitution of elimination
- Find the distance between the POI and point C
Find the center of the circle with points A, B, and C being on the circle
- Assuming AB and BC are chords on the circle, we find their slopes
- Get the perpendicular slope of these chords and the midpoint
- Using the midpoint and perpendicular lines of these slopes, get an equation of the right bisector of these chords
- Find the POI of these two lines and there is your center of the circle
MPM2D1 MPM2D1 MPM2D1