Coordinates, Volumes, and 3D Figures
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What direction are the quadrants labeled on the coordinate plane?
Counterclockwise. Starting with 1 in upper right.
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
If the slope = pos value, line points...
up to right
If the slope = neg value, line points...
down to right
In Coordinate Geometry: x = 0 & y = 0, only when...
b = 0. Otherwise y = b
What is the formula to calculate the distance between any two points on a Coordinate plane?
√(x1-x2)2 + (y1-y2)2
What is the midpoint fomula for coordinate points?
- (x1-x2) , (y1-y2)
- __2 ,____2
In the coordinate plane, lines that are parallel will always have the same...
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)
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.
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.
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
inches2, feet2, miles2 etc. are measurements for...
inches3, feet3, miles3 etc. are measurements for...
How many faces are there for a rectangular solid?
6 (3 unique if length, height, and width are different).
What is the formula for a rectangular solid surface area?
2LW + 2 LH + 2WH
What is the formula for a cube surface area?
What is the formula for the volume of a cube?
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.
What is the Greatest Possible Distance within any rectangular box formula?
What is the Greatest Possible Distance within a cube formula?
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.
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.
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
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.
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.
The graph of a quadratic function (ex. x2-1) is called...
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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