Geometry 5 March 2013 Place your Coordinate Geometry Project on your desk. Check answers- ½ are posted. Questions? Warm Up- Linear Equations Review Handout Do handout Part A We will work on this for warm ups on Wed/Th and Friday. Complete handout will be due March 15 th.

Objective Students will review linear concepts. Students will take notes, participate in whole class discussion and solve problems.

Term Definition Distance Formula SlopeUse slope formula, slope triangle or table. Parallel lines have the same slope. Perpendicular line’s slopes are opposite reciprocals. Midpoint“Average”, Graph and/or use formula Coordinate Geometry Project Necessities

(x 1, y 1 ) (x 2, y 2 ) xy x1x1 y1y1 x2x2 y2y2 (y 2 -y 1 ) (x 2 -x 1 ) y2y2 y1y1 x2x2 x1x1 slope formula Developing the slope formula… y 2 -y 1 (x 2 – x 1 )

Point- Slope form of linear equation m(x 2 -x 1 )= 1 (y 2 –y 1 ) 1 (y 2 –y 1 )=m(x 2 -x 1 ) y 2 = y 1 + m(x 2 -x 1 ) y = y 1 + m(x-x 1 ) please write in your notes…. let (x 2, y 2 ) be “any” point on the line- so use (x, y)

Various Forms of an Equation of a Line. Slope-Intercept Form Standard Form Point-Slope Form

1. Parallel lines have the same slope Slope of Line A = Slope of Line B = Slope of Line A = Line A Line B Slope of Line B

2. Perpendicular lines slope at 90° Slope of Line A = Slope of Line B = Slope of Line A = Line A Line B Opposite Reciprocal of Line B

Write an equation in slope-intercept form for the line that contains the point (-3, 4), and is perpendicular to the graph of the equation. Y = 2x + 3 Step 1: Identify Slope Slope = _______ Perpendicular Slope = ______ Step 2: Write Equation y = m x + b ___ = ___(___) + b b = ____ Therefore, the equation is _____________

Write an equation in point-slope form for the line that contains the point (-3, 4), and is perpendicular to the graph of the equation. 12.Y = 2x + 3 Step 1: Identify Slope Slope = _______ Perpendicular Slope = ______ Step 2: Write Equation y = y 1 + m (x – x 1 ) y = ___ + ___(x -____) __________________________

perpendicular bisector

Perpendicular bisector A line or line segment that is perpendicular to a segment and bisects it. It CONTAINS the segment’s MIDPOINT It CONTAINS the segment’s MIDPOINT! 1) Find midpoint of segment. 2) Find slope of segment. 3) Find perpendicular slope (opposite reciprocal) 4) Find the equation of the line with the perpendicular slope and through the midpoint.

A line perpendicular to a line segment with slope m 1 = –4 has a slope of m 2 = – =. Use point-slope form with Midpoint of line segment is (x 1, y 1 ) = (–2, 3) m1m1 y = y 1 + m 2 (x – x 1 ) Use point-slope form. y = 3 + (x – (–2)) 1 4 Substitute for m 2, x 1, and y 1. y = 3 + (x +2) 1 4 Simplify. y = 3+ x Distributive property Write in slope-intercept form. Write equations of perpendicular lines

Practice Find the equation of the perpendicular bisector for the segment with endpoints (-2, 5) and (3, 10) STEPS 1) find midpoint 2) find slope 3) find perpendicular slope 4) find equation using y = mx + b (solve for b) OR y – y 1 = m(x – x 1 )

Practice Find perpendicular bisector for the line segment with endpoints 1) (-7, 4) and (1, 16) 2) (-2, -2) and (7, 10) 1) midpoint 2) slope 3) perpendicular slope 4) equation

parallel and perpendicular want more help? Khan Academy:

Work on Coordinate Geometry Project Finished? Work on problems page 466: