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What direction are the quadrants labeled on the coordinate plane?
Counterclockwise. Starting with 1 in upper right.
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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
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If the slope = pos value, line points...
up to right
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If the slope = neg value, line points...
down to right
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In Coordinate Geometry: x = 0 & y = 0, only when...
b = 0. Otherwise y = b
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What is the formula to calculate the distance between any two points on a Coordinate plane?
√(x1-x2)2 + (y1-y2)2
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What is the midpoint fomula for coordinate points?
- (x1-x2) , (y1-y2)
- __2 ,____2
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In the coordinate plane, lines that are parallel will always have the same...
slope
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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)
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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.
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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.
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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
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inches2, feet2, miles2 etc. are measurements for...
Area
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inches3, feet3, miles3 etc. are measurements for...
Volume
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How many faces are there for a rectangular solid?
6 (3 unique if length, height, and width are different).
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What is the formula for a rectangular solid surface area?
2LW + 2 LH + 2WH
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What is the formula for a cube surface area?
6s2
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What is the formula for the volume of a cube?
s3
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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.
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What is the Greatest Possible Distance within any rectangular box formula?
√(L2+W2+H2)
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What is the Greatest Possible Distance within a cube formula?
√(3L2)
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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.
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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.
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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
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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.
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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.
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The graph of a quadratic function (ex. x2-1) is called...
a parabola
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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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