Section

Content

Suggested Problems

Section 1.1

 Cartesian Plane
 Coordinates
 x coordinate; abscissa
 y coordinate; ordinate
 Quadrants


Section 1.2

 Distance Formula
 Applications
 Determine whether three points form the vertices of a right triange
 Determine whether three points are colinear
 Determine whether four points form the vertices of a parallelogram
 Determine whether four points form the vertices of a rhombus
 Determine whether four points form the vertices of a rectangle

Page 9: 5, 9, 15, 19, 23, 25

Section 1.3

 Point of Division Formulas
 Midpoint Formula

Page 18: 3, 9, 15, 21, 23

Section 1.4

 Inclination and Slope
 Slope formula
 Special Cases
 Slope of a horizontal line
 Slope of a vertical line


Section 1.5

 Parallel and Perpendicular Lines
 Criteria for two nonvertical lines to be parallel
 Criteria for two lines to be parallel if one of them is a vertical line
 Criteria for two nonvertical lines to be perpendicular
 Slopes are negative reciprocals
 Criteria for two lines to be perpendicular if one of them is a vertical line
 Applications
 Determine whether three points form the vertices of a right triange
 Determine whether three points are colinear
 Determine whether four points form the vertices of a parallelogram
 Determine whether four points form the vertices of a rhombus
 Determine whether four points form the vertices of a rectangle
 Determine whether two lines are parallel, coincident, perpendicular or none of the above

Page 28: 1, 3, 5, 11, 15, 19, 25, 30

Section 1.6

 Angle from One Line to Another
 Formula for the tangent of the angle between two nonvertical lines
 Given two nonvertical lines find the slope of the line which bisects the angle between the two lines

Page 35: 3, 9, 17

Section 1.7

 Graphs of Equations
 Points of Intersections of Graphs of Equations
 Function

Page 42: 3, 6, 9, 13, 17, 21, 25, 31

Section 2.1

 Directed Line Segment
 Vector
 Geometric definition of the sum of two vectors
 Parallelogram law for sum of two vectors
 Geometric definition of the difference of two vectors
 Length of a vector
 Geometric definition of a scalar multiple of a vector
 Theorem 2.2 Algebraic properties of sum, difference and scalar multiples of vectors
 Geometric definition of a unit vectors
 Standard basis vectors
 Theorem 2.3 Every vector can be written (as a unique) sum of scalar multiples of the standard basis vectors
 Algebraic rule for the sum of two vectors (in terms of components)
 Algebraic rule for the scalar multiple of a vector (in terms of components)
 Algebraic rule for the length of a vector

Page 60: 1, 3, 23, 25, 39, 41

Section 2.2

 Dot Product
 Theorem 2.6 Algebraic properties of dot product
 Angle between two nonzero vectors
 Theorem 2.7 Relationship between dot product and the angle between two vectors
 Theorem 2.8 Two nonzero vectors are perpendicular if and only if their dot product is zero
 Projection of a vector u onto a vector v

Page 69: 1, 9, 13, 17, 21, 29
