Honors Geometry 12 March 2012WarmWarm Up (5 minutes) Up (5 minutes)

1) Find the slope between (-3, -4) and (-6, -9) using the slope formula,

USE 1) formula 2) substitute 3) math 4) units

2) Simplify the radicals. a) b) c)

32 45 3 18

2 1

2 1

y ym

x x

ObjectiveStudents will use coordinate geometry formulas to

help determine the most specific name for quadrilaterals.

Students will take notes, and work with their group to present their solution on poster paper.

projects Coordinate Geometry Project DUE March 13th

QUESTIONS?

REVISIONS for DSH Kribz, due MARCH 13

Honors Geometry 4th Quarter Project DETAILS- PROPOSAL APPLICATION- ONLINEONLINE Preliminaries– due March 13 Final project due- May 8th

video, song, skit, tutorial, rap, dance…. other?

Homework due Friday

TEST on coordinate geometry/ Pythagorean theorem on FRIDAY

DO page 512: 1- 10, 13, 18

Point- Slope form of linear equation2 1

2 1

y ym

x x

m(x2-x1)= y2 –y1

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)

Using the point-slope formula

Example: Given a point on a line and the slope, find the equation of the line:

a) (2, 3) m = 2

y = y1 + m(x-x1) point-slope formula

y = 3 + 2(x -2) substitute x1 = 2, y1 = 3 and m = 2

y = 3 + 2x – 4 distributive property

y = 2x – 1 combine like terms

please write

in your notes

we can also use y =mx + b slope-intercept form of an equation of a line

3 = 2(2) + b substitute

3 = 4 + b evaluate-4 = -4 subtract 4 from both sides-1 = b

Equation? y = 2x - 1

y = mx + b slope-intercept eqtn

Example: Given a point on a line and the slope, find the equation of the line:a) (2, 3) m = 2

please write in

your notes

Name Formulaslope

point-slopeequation of a line

y = y1 + m(x-x1)

slope-interceptequation of a line

y = mx + b

midpoint

distance formula

2 1

2 1

y ym

x x

1 2 1 2( , )2 2

x x y y

2 22 1 2 1( ) ( )d x x y y

Finding the Distance Between Two Points

Using the Pythagorean theorem

(x 2 – x 1) 2 + ( y 2 – y 1) 2 = d 2

THE DISTANCE FORMULA

The distance d between the points (x 1, y 1) and (x 2, y 2) is

d = (x 2 – x 1) 2 + ( y 2 – y 1) 2

Solving this for d produces the

distance formula.

You can write the equation

a 2 + b 2 = c 2

x 2 – x 1

y2 – y1

d

x

y

C (x 2, y 1 )

B (x 2, y 2 )

A (x 1, y 1 )

The steps used in the investigation can be used to develop a general formula for the distance between two points A(x 1, y 1) and B(x 2, y 2).

Applying the Distance Formula

A player kicks a soccer ball that is 10 yards from a sideline and 5 yards from a

goal line. The ball lands 45 yards from the same goal line and 40 yards from

the same sideline. How far was the ball kicked?

The ball is kicked from the point (10, 5),

and lands at the point (40, 45). Use the

distance formula.

d = (40 – 10) 2 + (45 – 5) 2

= 900 + 1600 = 2500 = 50

The ball was kicked 50 yards.

SOLUTION

Finding the Midpoint Between Two Points

The midpoint of a line segment is the point on the segment that is equidistant

from its end-points. The midpoint between two points is the midpoint of the line

segment connecting them.

THE MIDPOINT FORMULA

The midpoint between the points (x 1, y 1) and (x 2, y 2) isx 1 + x 2

2( )y 1 + y 2

2,

Applying the Midpoint Formula

You are using computer software to design a video game. You want to place

a buried treasure chest halfway between the center of the base of a palm

tree and the corner of a large boulder. Find where you should place the

treasure chest.

SOLUTION

Assign coordinates to the locations of the two landmarks. The center of the palm tree is at (200, 75). The corner of the boulder is at (25, 175).

Use the midpoint formula to find the point that is halfway between the two landmarks.

1

2

25 + 2002( )175 + 75

2,225

2( )2502,= = (112.5, 125)

(25, 175)

(200, 75)

(112.5, 125)

practiceCW paper: everyone do pg. 504: 1 – 3Then each group will PREPARE A POSTER presenting your work for the following problems:Use the definitions of polygons to justify naming your quadrilateralGroups 1 and 7: #7 Groups 2 and 6: #8Groups 3 and 5: #9 Groups 4 and 8: #10

NOTE: all students must do your assigned problem w/ supporting work ON YOUR OWN GRAPH PAPER

debriefhow did we use Pythagorean formula to develop the distance formula?

how did we use the slope formula to develop the point-slope form of an equation of a line?

what is easy?

what is still confusing?