Mathematics & Statistics Texas Tech University Kent Pearce Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Voice: (806)742-2566 x 226 FAX: (806)742-1112 Email: kent.pearce@ttu.edu

 Math 1350 Analytical Geometry Fall 2014 Riddle Analytical Geometry Brooks/Cole

Review Exam I

 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 co-linear 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 Mid-point 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 non-vertical lines to be parallel Slopes are equal Criteria for two lines to be parallel if one of them is a vertical line Criteria for two non-vertical 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 co-linear 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, co-incident, 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 non-vertical lines Given two non-vertical 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 Domain Range Page 42: 3, 6, 9, 13, 17, 21, 25, 31 Section 2.1 Directed Line Segment Vector Representative 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 Components of a vector 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 non-zero vectors Theorem 2.7 Relationship between dot product and the angle between two vectors Theorem 2.8 Two non-zero 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

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