Geometry 5 March 2013

Place your Coordinate Geometry Project on your desk. Check answers- ½ are posted. Questions?

Warm Up- Linear Equations Review HandoutWarm Up- Linear Equations Review HandoutDo handout Part ADo handout Part A

We will work on this for warm ups on Wed/Th and Friday. Complete handout will be due March 15th.

Objective

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

Term DefinitionDistance Formula

Slope Use 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

2 22 1 2 1AB x x y y

2 1

2 1

y yy risemx run x x

1 2 1 2int int;

2 2midpo midpox x y yx y

(x1, y1)

(x2, y2)x yx1 y1

x2 y2

(y2-y1)(x2-x1)

2 1

2 1

y ymx x

y2

y1

x2x1

slope formula

Developing the slope formula…

y2-y1

(x2 – x1)

Point- Slope form of linear equation2 1

2 1

y ymx x

m(x2-x1)= 1(y2 –y1)1(y2 –y1)=m(x2-x1)

y2 = y1 + m(x2-x1)

y = y1 + m(x-x1)

please write in your notes….

let (x2, y2) be “any” point on the line- so use (x, y)

1

Various Forms of an Equation of a Line.

Slope-Intercept Form

Standard Form

Point-Slope Form

slope of the lineintercept

y mx bmb y

, , and are integers0, must be postive

Ax By CA B CA A

1 1

1 1

slope of the line, is any point

y y m x x

mx y

1. Parallel lines have the same slope

Slope of Line A =

Slope of Line B =

Slope of Line A =

Line A

Line B

1

1

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 BOpposite Reciprocal

of Line B

12

21

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 + 3Step 1: Identify SlopeSlope = _______Perpendicular Slope = ______Step 2: Write Equationy = m x + b___ = ___(___) + bb = ____Therefore, the equation is _____________

21

2

4 -31

2

52 1 5

2 2y x

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 + 3Step 1: Identify SlopeSlope = _______Perpendicular Slope = ______Step 2: Write Equationy = y1 + m (x – x1)y = ___ + ___(x -____)__________________________

perpendicular bisector

Perpendicular bisectorA line or line segment that is perpendicular to a segment and bisects it. It CONTAINS the segment’s MIDPOINTIt 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 m1 = –4 has a slope of m2 = – = . Use point-slope form with

Midpoint of line segment is (x1, y1) = (–2, 3)

14

1m1

y = y1 + m2(x – x1) Use point-slope form.

y = 3 + (x – (–2))14 Substitute for m2, x1, and y1.

y = 3 + (x +2)14 Simplify.

y = 3+ x +14

12 Distributive property

Write in slope-intercept form.

Write equations of perpendicular lines

1 74 2

y x

Practice

Find the equation of the perpendicular bisector for the segment with endpoints (-2, 5) and (3, 10)

STEPS1) find midpoint2) find slope3) find perpendicular slope4) find equation using y = mx + b (solve for b)OR y – y1 = m(x – x1)

Practice

Find perpendicular bisector for the line segment with endpoints1) (-7, 4) and (1, 16)2) (-2, -2) and (7, 10)

1) midpoint2) slope3) perpendicular slope4) equation

parallel and perpendicularwant more help?http://www.mathvids.com/lesson/mathhelp/83-parallel-and-perpendicular-linesKhan Academy: http://www.youtube.com/watch?v=9hryH94KFJA&feature=related

Work on Coordinate Geometry Project

Finished? Work on problems page 466: 1 - 10