USE 1) formula 2) substitute 3) math 4) units Honors Geometry 12 March 2012 Warm 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)

Objective Students 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- ONLINE 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 equation please write in your notes…. m(x2-x1)= y2 –y1 y2 –y1=m(x2-x1) y2 = y1 + m(x2-x1) let (x2, y2) be “any” point on the line- so use (x, y) y = y1 + m(x-x1)

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 please write in your notes 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

we can also use y =mx + b slope-intercept form of an equation of a line 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 y = mx + b slope-intercept eqtn 3 = 2(2) + b substitute 3 = 4 + b evaluate -4 = -4 subtract 4 from both sides -1 = b Equation? y = 2x - 1

y = y1 + m(x-x1) y = mx + b Name Formula slope point-slope equation of a line y = y1 + m(x-x1) slope-intercept y = mx + b midpoint distance formula

Finding the Distance Between Two Points 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). Using the Pythagorean theorem x 2 – x 1 y2 – y1 d x y C (x 2, y 1 ) B (x 2, y 2 ) A (x 1, y 1 ) a 2 + b 2 = c 2 You can write the equation (x 2 – x 1) 2 + ( y 2 – y 1) 2 = d 2 Solving this for d produces the distance formula. 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

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? SOLUTION 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.

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

( ) ( ) , , 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 (25, 175) 1 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). (112.5, 125) (200, 75) 2 Use the midpoint formula to find the point that is halfway between the two landmarks. 25 + 200 2 ( ) 175 + 75 , 225 2 ( ) 250 , = = (112.5, 125)

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

debrief how 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?