Honors Geometry 22 February 2013
Warm up: 1) Find the base of the trapezoid if A ≈ 22.5 yd2
a) 2 ft b) 10 ft c) 12 ft Show your work to justify your answer.
2) SOLVE for n:
h = 15 ft
17 ft
8 1 2 9 3n n
ObjectiveStudents will use the Pythagorean formula to solve problems and discover /apply the distance formula
Students will take notes and work with their groups to solve and present problems.
Homework due TODAY, February 22:Homework due TODAY, February 22:Khan Academy- Proficiency in 4 skillsKhan Academy- Proficiency in 4 skills
SEE HANDOUT FOR DETAILSSEE HANDOUT FOR DETAILS1- from each column1- from each column
paragraph for each topicparagraph for each topic
Homework due Tuesday
pg. 499: 4, 5, 7pg. 504: 2, 5, 6
pg. 509: 1 – 8 evens
Need to take last week’s quiz
P2: CrystalP3: Lathecia, Camille, David, AshP5: Keyla, Allison, DomP6: Kawther, Sophie, Nabaa, Cooper, Claire, Angelica
Types of Slope
PositiveNegative
Zero
Undefinedor
No Slope
If given 2 points on a line, you may findthe slope using theformula y2 – y1
x2 – x1
://www.youtube.com/watch?v=PPXx-43ke-g
m =
slope-intercept form,y = mx + b.
slopey-intercept
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
Let's find the distance between two points.
So the distance from (-6,4) to (1,4) is 7.
If the points are located horizontally from each other, the y coordinates will be the same. You can look to see how far apart the x coordinates are.
(1,4)(-6,4)
7 units apart
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
What coordinate will be the same if the points are located vertically from each other?
So the distance from (-6,4) to (-6,-3) is 7.
If the points are located vertically from each other, the x coordinates will be the same. You can look to see how far apart the y coordinates are.
(-6,-3)
(-6,4)
7 units apart
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
But what are we going to do if the points are not located either horizontally or vertically to find the distance between them?
Let's add some lines and make a right triangle.
This triangle measures 4 units by 3 units on the sides. If we find the hypotenuse, we'll have the distance from (0,0) to (4,3)
Let's start by finding the distance from (0,0) to (4,3)
?
4
3
The Pythagorean Theorem will help us find the hypotenuse
222 cba 222 34 c2916 c
5c
5
So the distance between (0,0) and (4,3) is 5 units.
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
Now let's generalize this method to come up with a formula so we don't have to make a graph and triangle every time.
Let's add some lines and make a right triangle.
Solving for c gives us:
Let's start by finding the distance from (x1,y1) to (x2,y2)
?
x2 - x1
y2 – y1
Again the Pythagorean Theorem will help us find the
hypotenuse
222 cba (x2,y2)
(x1,y1)
22
122
12 cyyxx
2122
12 yyxxc
This is called the distance formula
2122
12 yyxxc
Let's use it to find the distance between (3, -5) and (-1,4)
(x1,y1) (x2,y2)
3-1 -54
2294 c 8116 8.997
CAUTION!
You must do the brackets first then powers (square the numbers) and then add together BEFORE you can square root
Don't forget the order of operations!
means approximately equal to
found with a calculator
Plug these values in the distance formula
Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint.
www.slcc.edu
Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.
Stephen CorcoranHead of MathematicsSt Stephen’s School – Carramarwww.ststephens.wa.edu.au
Term Definition
Distance FormulaWRITE IN YOUR
NOTES
The distance between points and Is given by the formula:
Chapter 9 Pythagorean Theorem
1 1,A x y 2 2,B x y
2 2
2 1 2 1AB x x y y
a
Find the distance between each pair of pointsFind the distance between each pair of points
1, 2 , 11, 7
2 2
2 1 2 1AB x x y y
9, 6 , 3,10
Required: 1) formula 2) substitution 3) do math 4) units
Find the distance between the two points:
1)
2)
ClassworkDO page 504: 1, 3DO page 504: 1, 3GROUPS- 1) Each student needs to do the work on their own paper. Use graph paper.2) Find distance and slope for each side of your quadrilateral using the formulas. Find the linear equation for the line containing each side.Groups 1 & 8: # 7Groups 1 & 8: # 7 Groups 2 & 7: # 8Groups 3 & 5: # 9Groups 3 & 5: # 9 Groups 4 & 6: # 10Groups 4 & 6: # 10
debrief
how did we use Pythagorean formula to develop the distance formula?
what is easy?
what is still confusing?
