Coordinate Geometry Flashcards
Median
Vertices to the midpoint of opposite side
Altitude
Perpendicular to the opposite side
Perpendicular Bisector
Cuts opposite side in half but does not have to come from Vertice
Write an equation of line parallel to 5x-8y+2=0 with coordinates (-1,7)
Y-7 = 5/8 (x-1) (x+1??)
How to find a value collinear to other values?
Find the average (median) of the other 2 values
Bh/2
Area of a triangle
Sum of the lengths of the 3 sides
Perimeter of a triangle
2
S, 4s
Area & Perimeter of a square
A= bh (lw)
Area of a rectangle, rhombus, or parallelogram
Perimeter of a rectangle, rhombus, and/or parallelogram
P= 2b+ 2h
How to prove a triangle is scalene
Use distance formula 3 times to prove each side has a different length
How to prove a triangle is isosceles
Distance formula 3 times to prove 2 sides are congruent
How to prove a triangle is equilateral
Distance formula 3 times to prove all 3 sides are equal to each other
How to prove a right triangle
Use slope formula 3 times to prove 2 sides are perpendicular (the slopes will be negative reciprocals of the other)
How to prove a parallelogram is a quadrilateral
Use slope formula 4 times to prove both pairs of opposite sides are parallel
How to prove a rectangle is a quadrilateral
Use slope formula 4 times to prove it’s a parallelogram and consecutive sides are perpendicular
How to prove a rhombus is a quadrilateral
Use slope formula 6 times (4 for each side + diagonals) to prove it’s a parallelogram (both pairs of opposite sides are parallel) and diagonals are perpendicular to each other
How to prove a square is a quadrilateral
Slope formula 6 times to prove it’s a parallelogram, 2 consecutive sides are perpendicular and diagonals are perpendicular (prove it’s a parallelogram, rectangle, and rhombus)
How to prove a trapezoid is a quadrilateral
Use slope formula 4 times to prove at least one pair of opposite sides are parallel
How to prove an isosceles trapezoid is a parallelogram
Slope formula 4x and distance formula 2x to prove it’s a trapezoid and either the non parallel sides or diagonals are equal
Proof an isosceles trapezoid is a parallelogram
prove it’s a trapezoid and either the non parallel sides or diagonals are equal
Prove a trapezoid is a quadrilateral
prove at least one pair of opposite sides are parallel
Prove a square is a quadrilateral
prove it’s a parallelogram, 2 consecutive sides are perpendicular and diagonals are perpendicular (prove it’s a parallelogram, rectangle, and square)
Prove a rhombus is a quadrilateral
prove it’s a parallelogram (both pairs of opposite sides are parallel) and diagonals are perpendicular to each other
Prove a rectangle is a quadrilateral
prove it’s a parallelogram and consecutive sides are perpendicular!!!
Prove a parallelogram is a quadrilateral
prove both pairs of opposite sides are parallel
how to do a question in which it gives 3 points with a variable and asks to prove something is a right triangle
1) find slope of coordinates w/out variable
2) find negative reciprocal of this slope and set equal to one of the coordinates with said variable
3) division, multiplication, etc. until x=
How to find median (random pair of coordinates from line with slope, made up from vertex & midpoint of that line)
1) find MIDPOINT!!!! of the line the median intersects
2) take those coordinates + the vertex’s coordinates to find slope of the median
3) use THIS SLOPE and a RANDOM pair of coordinates from the line to set up the equation
How to find altitude (slope of line, flipped and negated, with vertex of triangle)
1) find slope of the side the altitude intersects and flip & negate it
2) Use the vertex (where altitude begins) and the slope to set up an equation
How to find perpendicular bisector (flipped and negated slope of the line and the midpoint’s coordinates)
1) Find side of the slope the side that is bisected and flip & negate it
2) FIND MIDPOINT OF THE SIDE THAT WAS BISECTED !!
3) use the midpoint of that side and slope to set up equation
Setting up equations
Median: random point from the line & slope (using vertex and midpoint of line as coordinates for slope)
Altitude: slope of line that’s flipped and negated with the coordinates of the vertex
Perpendicular Bisector: slope of line that’s flipped and negated + the midpoint of that same line
area of a trapezoid
a+b/
2h
area of an isosceles trapezoid
Area = 1/2 (a+b) (h)
