Unit 9 - Coordinate Geometry Flashcards
What is the formula for finding slope?
Y2 - Y1/X2 - X1
What is the formula for slope - intercept form?
y = mx + b
What is the formula for Point - Slope Form?
y - k = m (x - h)
What is an acronym that helps you remember the point slope acronym?
y - x = m (x - h)
You
Know
My
X - ray
Helps
How do you know the slope for perpendicular lines?
Negative Reciprocal to the Segment
What is the slope of a vertical line & formula?
- VUX
- Undefined
- X = _
What is the slope of a horizontal line & formula?
- HOY
- Zero
- Y = _
How do you know the slope for parallel lines?
Slopes are the Same
What is the midpoint formula?
[ (x1 + x2) /2, (y1 + y2)/2 ]
How to get Perpendicular Bisector Equation (4)
- Find Midpoint (MP Formula)
- Find slope of segment
- Take negative reciprocal
- Plug coordinates to Point - Slope form
How do you find the equation of a median of a triangle? (3)
- Find Midpoint (Use midpt. formula)
- Find slope of median (mp & vertex)
- Plug in the coordinates and slope to point - slope form
How do you find the equation of an altitude? (4)
- Find slope of the opp. side
- Use the negative reciprocal
- Find coordinates of the vertex
- Plug to Point - Slope form
What to note about fractions?
DON’T LEAVE THE DECIMAL IN THE FRACTION
What is the another name for perpendicular lines?
Normal Lines
How do you find the perimeter of a triangle on a coordinate grid?
- Box the Triangle (Area of Rectangle)
- Find hypotenuse of 3 surrounding triangles
- H1 + H2 + H3 = P of Triangle
When can 1/2 bh formula be used for a triangle?
Only if the base and the height of the triangle are perpendicular (right triangle)
How do you find the area of a triangle on the coordinate grid? (4)
Use the Shoelace Formula
A = 1/2 [x1y1 + x2y3 + x3y1 - y1x2 - y2x3 - y3x1]
- Line coordinates of triangle to 2 columns
- Each column is x coordinates & y coordinates
- Cross multiply from the left, and add the products
- Switch to the right & switch the signs of the products (subtract them)
What is the distance formula?
d = √(x₂ - x₁)² + (y₂ - y₁)²
What are the three properties we can utilize for coordinate proofs?
- Slope
- Midpoint
- Distance
What is slope used for in coordinate proofs?
Parallel & Perpindicular Lines
What is distance used for in coordinate proofs?
Congruent side lengths
What is midpoint used for in coordinate proofs?
Diagonals bisect each other
How do you prove an equilateral triangle in coordinate proofs?
3 congruent sides = 3 Distances
How do you prove an isosceles triangle in coordinate proofs?
2 congruent sides = 2 Distances
How do you prove a right triangle in coordinate proofs?
1 rt angle= 2 slopes
How do you prove a trapezoid in coordinate proofs?
1 set of opposite sides are parallel = 2 Slopes
How do you prove an isosceles trapezoid in coordinate proofs? (3)
- Prove Trapezoid
- Congruent Legs = 2 Distance
- Congruent Diagonals = 2 Distance
How do you prove a parallelogram in coordinate proofs? (4)
- 2 sets of opp. sides congruent = 4 Distance
- 2 sets of opp. sides parallel = 4 Slope
- Diagonals bisect e/o = 2 midpoint
- 1 set of opp. sides congruent & parallel = 2 Distance & 2 Slope
How do you prove a rectangle in coordinate proofs? (3)
- Prove Parallelogram
- Diagonals Congruent = 2 Distance
- 1 rt angle = 2 Slope
How do you prove a rhombus in coordinate proofs?
- Prove Parallelogram
- Consecutive Sides Congruent = 2 Distance
- Diagonals Perpindicular = 2 Slope
How do you prove a square in coordinate proofs?
- Prove Parallelogram
- Prove Rectangle
- Prove Rhombus
How do you prove a kite in coordinate proofs?
- 2 Sets Cons. Sides Congruent = 4 Distance
- Diagonals Perpendicular = 2 Slope
