Coordinates, Volumes, and 3D Figures

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Author:
JanineG14
ID:
90356
Filename:
Coordinates, Volumes, and 3D Figures
Updated:
2011-06-20 01:35:34
Tags:
Geometry Coordinates Volumes 3D Figures
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Description:
Geometry (Coordinates, Volumes, and 3D Figures)
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  1. What direction are the quadrants labeled on the coordinate plane?
    Counterclockwise. Starting with 1 in upper right.
  2. All algebraic equations that are linear (no exponents) can be mapped on the coordinate plane as a straight line. With what equation?
    y = mx + b

    • m = slope
    • b = y-intercept
    • -b/m = x-intercept
  3. Slope =
    • change in y
    • change in x

    • Y2-Y1
    • X2-X1
  4. If the slope = pos value, line points...
    up to right
  5. If the slope = neg value, line points...
    down to right
  6. In Coordinate Geometry: x = 0 & y = 0, only when...
    b = 0. Otherwise y = b
  7. What is the formula to calculate the distance between any two points on a Coordinate plane?
    √(x1-x2)2 + (y1-y2)2
  8. What is the midpoint fomula for coordinate points?
    • (x1-x2) , (y1-y2)
    • __2 ,____2
  9. In the coordinate plane, lines that are parallel will always have the same...
    slope
  10. In the coordinate plane, lines that are perpindicular to each other will have slopes that are...
    • Negative reciprocals of each other. i.e. the product of their slopes will = -1.
    • ex: y = -1/2x + 2 & y = 2x + 4
    • m= -1/2 & 2 .... (-1/2 * 2 = -1)
  11. You can determine the equation of a line if you are given 1 of the following:
    • 1) Any two points on the line
    • 2) One point on the line AND the slope
    • 3) One point on the line AND the slope OR equation of a line perpindicular to that line.
    • 4) One point on the line AND the slope OR equation of a line parallel to that line.
  12. If I ever receive a question that is not linear (contains a squared variable) on a coordinate plane question, what will be produced and what should I use?
    A Circle or Curved Line will be made. Use an input/output method to determine what the figure will look like.
  13. How do you find the volume of any 3D figure?
    • Multiply the known base (rectangle, circle, or triangle area etc.) by the height.
    • (area of base) * height = volume
  14. inches2, feet2, miles2 etc. are measurements for...
    Area
  15. inches3, feet3, miles3 etc. are measurements for...
    Volume
  16. How many faces are there for a rectangular solid?
    6 (3 unique if length, height, and width are different).
  17. What is the formula for a rectangular solid surface area?
    2LW + 2 LH + 2WH
  18. What is the formula for a cube surface area?
    6s2
  19. What is the formula for the volume of a cube?
    s3
  20. Remember: To figure out surface area of other 3D figures (not a rectangular solid), depend on knowledge of basic geometry and the definition of the surface area to solve.
  21. What is the Greatest Possible Distance within any rectangular box formula?
    √(L2+W2+H2)
  22. What is the Greatest Possible Distance within a cube formula?
    √(3L2)
  23. In coordinate planes, if the line is a vertical line, what is the equation?
    x = a (where a is the x-intercept) and the slope is not defined.
  24. In regards to the connection b/w lines on a coordinate plane & solutions of two linear equations with two unknowns: If two linear equations w/ two unknowns have a unique solution, the the graphs of the equations are...
    two lines that intersect in one point, which is the solution.
  25. In regards to the connection b/w lines on a coordinate plane & solutions of two linear equations with two unknowns: If two linear equations are equivalent the graphs of the equations are...
    the same line with infinitely many points or solutions
  26. In regards to the connection b/w lines on a coordinate plane & solutions of two linear equations with two unknowns: If the equations have no solution, then they represent...
    parallel lines, which don't intersect.
  27. Can functions be plotted in the coordinate plane? If so, how?
    • Yes, they can. Set y = f(x).
    • So f(x) = x2-1 becomes y = x2-1

    And use an input/output method/graph when needed.
  28. The graph of a quadratic function (ex. x2-1) is called...
    a parabola
  29. What's the first step to find the y-intercept or x-intercept in an equation?
    set x=0 (for y-intercept), or y=0 (for x-intercept)

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