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

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