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# Criswell Geometry

### Vocabulary and Formulas to Remember (Chapter 2)

QuestionAnswer
Slope " Average Rate of Change" m = (∆y /∆x) m = rise / run m = (y2–y1) / (x2–x1)
Midpoint MP = ( ave x values , ave y values ) MP = ( [x1+x2] / 2 , [y1+y2] / 2 )
Distance Formula d= √ [ (y2–y1)^2 + (x2–x1)^2 ] d=√ [ (∆y )^2 + (∆x)^2 ]
Discriminant = b^2 – 4(a)(c) if result is negative, then no solutions. if result is zero, then one rational root "double root". if result is positive non-square value, then two irrational roots. if result is positive square value, then two rational roots.
Quadratic Formula x = (–b ± √ [ b^2–4(a)(c)] ) / (2a) x = (–b ± √ [ discriminant] ) / (2a)
Linear Forms 1) y = mx + b or y = (∆y / ∆x) x + b. "slope intercept" 2) Ax + By = C "standard" 3) (y–k) = m (x–h) "point slope"
Criteria for Standard Form Linear Equations 1) Must be in "Ax + By = C" form 2) where A, B, & C are integers 3) and "A" must be a positive value m = –A / B or first number over the second and "change the sign".
Parallel Slopes The slopes of parallel " // "lines are the SAME! Examples: m = 4/5, m // = 4/5 m = –2/3, m // = –2/3
Perpendicular Slopes The slopes of perpendicular "⊥" lines are OPPOSITE RECIPROCALS! Examples: m = 2/7, m ⊥ = –7/2 m = –3/5, m ⊥ = 5/3
What is the ratio for Sine? opposite side to focused angle / hypotenuse
What is the ratio for Cosine? adjacent side to focused angle / hypotenuse
What is the ratio for Tangent? opposite side to focused angle / adjacent side to focused angle
Solving Systems of Equations Be able to put data into the matrix editor to solve a system. (rref) Be able to interpret (read) the results. This would include specific solutions, no solutions, and infinite solutions.
Partitioning a line segment Be able to read and understand how ratios can be transformed into fractions. This includes part to part and part to whole ratios. Understanding the context of the problem is crucial. Example: part to part 3:4 => 3/7 part to whole 5:12 => 5/12
Be able to read and interpret solutions from a Matrix Understand the difference between a unique solution, infinite solutions, and the empty set as it relates to reading a matrix.
Created by: Troy.Criswell
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