# MPM2D Grade 10 Math Analytic Geometry Test

Midpoint

• M=((x1+x2)/(2)),((y1+y2)/(2))

Length

• L=√(x2-x1)^2+(y2-y1)^2

Must Know: 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

1. find slope, then y-intercept of the line segment AB
2. Find the perpendicular slope of line AB
3. Match up coordinates of C to the perpendicular slope in y=mx+b format
4. Find POI of line C and AB to see where ^ line intersects with line AB through substitution of elimination
5. 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

1. Assuming AB and BC are chords on the circle, we find their slopes
2. Get the perpendicular slope of these chords and the midpoint
3. Using the midpoint and perpendicular lines of these slopes, get an equation of the right bisector of these chords
4. Find the POI of these two lines and there is your center of the circle