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A Geometry > Unit 9 - Coordinate Geometry > Flashcards

Unit 9 - Coordinate Geometry Flashcards

1
Q

What is the formula for finding slope?

A

Y2 - Y1/X2 - X1

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2
Q

What is the formula for slope - intercept form?

A

y = mx + b

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2
Q

What is the formula for Point - Slope Form?

A

y - k = m (x - h)

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3
Q

What is an acronym that helps you remember the point slope acronym?

A

y - x = m (x - h)

You

Know

My

X - ray

Helps

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4
Q

How do you know the slope for perpendicular lines?

A

Negative Reciprocal to the Segment

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5
Q

What is the slope of a vertical line & formula?

A
  1. VUX
  2. Undefined
  3. X = _
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5
Q

What is the slope of a horizontal line & formula?

A
  1. HOY
  2. Zero
  3. Y = _
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5
Q

How do you know the slope for parallel lines?

A

Slopes are the Same

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6
Q

What is the midpoint formula?

A

[ (x1 + x2) /2, (y1 + y2)/2 ]

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7
Q

How to get Perpendicular Bisector Equation (4)

A
  1. Find Midpoint (MP Formula)
  2. Find slope of segment
  3. Take negative reciprocal
  4. Plug coordinates to Point - Slope form
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8
Q

How do you find the equation of a median of a triangle? (3)

A
  1. Find Midpoint (Use midpt. formula)
  2. Find slope of median (mp & vertex)
  3. Plug in the coordinates and slope to point - slope form
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9
Q

How do you find the equation of an altitude? (4)

A
  1. Find slope of the opp. side
  2. Use the negative reciprocal
  3. Find coordinates of the vertex
  4. Plug to Point - Slope form
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10
Q

What to note about fractions?

A

DON’T LEAVE THE DECIMAL IN THE FRACTION

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11
Q

What is the another name for perpendicular lines?

A

Normal Lines

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12
Q

How do you find the perimeter of a triangle on a coordinate grid?

A
  1. Box the Triangle (Area of Rectangle)
  2. Find hypotenuse of 3 surrounding triangles
  3. H1 + H2 + H3 = P of Triangle
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13
Q

When can 1/2 bh formula be used for a triangle?

A

Only if the base and the height of the triangle are perpendicular (right triangle)

14
Q

How do you find the area of a triangle on the coordinate grid? (4)

A

Use the Shoelace Formula
A = 1/2 [x1y1 + x2y3 + x3y1 - y1x2 - y2x3 - y3x1]

  1. Line coordinates of triangle to 2 columns
  2. Each column is x coordinates & y coordinates
  3. Cross multiply from the left, and add the products
  4. Switch to the right & switch the signs of the products (subtract them)
15
Q

What is the distance formula?

A

d = √(x₂ - x₁)² + (y₂ - y₁)²

16
Q

What are the three properties we can utilize for coordinate proofs?

A
  1. Slope
  2. Midpoint
  3. Distance
17
Q

What is slope used for in coordinate proofs?

A

Parallel & Perpindicular Lines

18
Q

What is distance used for in coordinate proofs?

A

Congruent side lengths

19
Q

What is midpoint used for in coordinate proofs?

A

Diagonals bisect each other

20
Q

How do you prove an equilateral triangle in coordinate proofs?

A

3 congruent sides = 3 Distances

21
Q

How do you prove an isosceles triangle in coordinate proofs?

A

2 congruent sides = 2 Distances

22
Q

How do you prove a right triangle in coordinate proofs?

A

1 rt angle= 2 slopes

23
Q

How do you prove a trapezoid in coordinate proofs?

A

1 set of opposite sides are parallel = 2 Slopes

24
Q

How do you prove an isosceles trapezoid in coordinate proofs? (3)

A
  1. Prove Trapezoid
  2. Congruent Legs = 2 Distance
  3. Congruent Diagonals = 2 Distance
25
Q

How do you prove a parallelogram in coordinate proofs? (4)

A
  1. 2 sets of opp. sides congruent = 4 Distance
  2. 2 sets of opp. sides parallel = 4 Slope
  3. Diagonals bisect e/o = 2 midpoint
  4. 1 set of opp. sides congruent & parallel = 2 Distance & 2 Slope
26
Q

How do you prove a rectangle in coordinate proofs? (3)

A
  1. Prove Parallelogram
  2. Diagonals Congruent = 2 Distance
  3. 1 rt angle = 2 Slope
27
Q

How do you prove a rhombus in coordinate proofs?

A
  1. Prove Parallelogram
  2. Consecutive Sides Congruent = 2 Distance
  3. Diagonals Perpindicular = 2 Slope
28
Q

How do you prove a square in coordinate proofs?

A
  1. Prove Parallelogram
  2. Prove Rectangle
  3. Prove Rhombus
29
Q

How do you prove a kite in coordinate proofs?

A
  1. 2 Sets Cons. Sides Congruent = 4 Distance
  2. Diagonals Perpendicular = 2 Slope

A Geometry (20 decks)

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