Geometry Notes G.2 Equations of Lines, Perpendicular Theorems Mrs. Grieser Name: _______________________________ Date: _____________ Block: _______ Writing Equations of Lines Review from Algebra 1: slope-intercept form of a linear equation _______________ 1) Write an equation of a line given a graph of a line. m = _________ Point-slope formula: ___________ point from line: ______________ slope-intercept equation: ____________ ____________ ____________ OR in this case, notice we know the y-intercept (b), and plug into y = mx + b __________ 2) Graph the equation: 3x + 4y = 12 Put in slope-intercept form: _________ Graph Alternatively, keep in standard form and find intercepts 3) Write an equation of a parallel line (slopes are ___________): Write an equation of a line that passes through point (-1, 1) that is parallel to the line with equation y = 2x – 3. o Slope of given equation:_________ o Slope of new line: _________ Point on new line: ________ o Equation of new line: 4) Write an equation of a perpendicular line (slopes are _________________________): Write an equation of a line that passes through point (2, 3) that is perpendicular to the line with equation y = -2x + 2. o Slope of given equation:_________ o Slope of new line: _________ Point on new line: ________ o Equation of new line: You try: a) Write an equation b) Graph 2x + 3y = 18. c) Write an equation d) Write an equation of the line. of the line that of a line that passes passes through through P(2, 3) and P(-2, 1) and is is perpendicular to parallel to y – 4 = -2(x + 3). 10x + 4y = -8. Geometry Notes G.2 Equations of Lines, Perpendicular Theorems Mrs. Grieser Page 2 Perpendicular Line Theorems If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. If two lines are perpendicular, then they intersect to form four right angles. If two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Perpendicular Transversal Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Lines Perpendicular to a Transversal Theorem In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. You Try: 1) Given <ABC <ABD, 2) Find the value of x. 3) Determine which lines, if what can you conclude any, must be parallel in the about <3 and < 4? diagram. Distance from a Point to a Line Distance from a point to a line is the length of the perpendicular segment from the point to the line. The distance between two parallel lines is the length of any perpendicular segment joining the two lines. Use the distance formula to find the length of the given point and the point where the line and perpendicular segment intersect. Distance formula: ________________________ Geometry Notes G.2 Equations of Lines, Perpendicular Theorems Mrs. Grieser Page 3 Examples: Round to the nearest tenth... a) Find the distance between lines: b) What is the distance between the graph of line and point (4,1)? Slope of lines_________ y x 1 Graph line Slope of segment:_____ Find equation of line through Point of intersection:______ point (4,1) perpendicular to Distance:__________ _______________ Where do lines intersect (set lines equal)? _________ Find distance between (4, 1) and point of intersection ____________________ You Try (round to the nearest tenth) ... a) Find the distance between the lines: b) Find the distance between the given point to the given line: (-6, 4) and y = -2x + 7 .