Download Math1 distance midpoint parallel perpendicular.notebook

Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Unit 2, Day 1
Relating Algebra to Geometry
May 14­1:24 PM
Do you remember Pythagorean Theorem???
b
c
In this formula, a and b are the lengths of two legs of the triangle, and c is the length of the hypotenuse.
a
Dec 7­2:14 PM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
The Pythagorean Theorem
We can use this equation to find the distance between two points on a graph...
Dec 7­2:18 PM
Dec 7­2:32 PM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Let's look at what we just did Dec 7­2:35 PM
Let's go even further back...
Dec 7­2:38 PM
3
Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
The formula we just found is called the distance formula, and can be used to find the distance between two points...
Dec 7­2:41 PM
Find the perimeter of triangle ABC.
Find the length of each segment (AB, BC, and CA) and then add the three lengths together.
Oct 25­10:22 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Find the length of each segment and then add the lengths together.
Oct 25­9:16 AM
Oct 25­9:15 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
On a different note, how did we find the mean (average) of two numbers?
Use a and b to represent the two numbers.
Dec 7­2:44 PM
Using the same idea, how can you find the midpoint of a segment on a graph?
Dec 7­2:47 PM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Start with finding the mean of the x values...
Dec 7­2:48 PM
Then find the mean of the y values...
Dec 7­2:51 PM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Finally, let's put our means together to find our midpoint...
M
x=1 y=2
The midpoint is at (1,2)
Dec 7­2:53 PM
So our formula to find the midpoint of a line segment is...
What is the midpoint of AB?
Dec 7­2:57 PM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
HW Page 594 # 2­24 even, 25,26,32
Nov 9­7:12 AM
Unit 2, Day 1
Parallel and Perpendicular Lines
(section 6.5 in your textbook)
Objectives:
• Determine if lines are parallel or perpendicular
Oct 25­8:32 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
What is the slope of this line?
Oct 25­11:11 AM
Oct 25­8:38 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Oct 25­8:40 AM
Two lines are parallel when their slopes are exactly
the same. Their y-intercepts cannot be the same
numbers.
y = 2/3 x - 7
y = 2/3 x - 4
Two lines are perpendicular when their slopes are the
opposite reciprocals of each other.
ex. 3/5 is the opposite reciprocal of -5/3.
Oct 25­8:40 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Two lines are perpendicular when their slopes are the
opposite reciprocals of each other.
ex. 3/5 is the opposite reciprocal of -5/3.
Match the opposite reciprocals
2/3
-3
3/2
2
-2
1/3
Oct 25­8:33 AM
Find both slopes and tell whether the lines
are parallel, perpendicular, or neither.
y = 4x + 3/4, y = (-1/4)x + 4
y = x/3 - 4, y = (1/3)x + 2
y = 5x,
y = -5x + 7
x = 2,
y=9
2x + y = 2 2x + y = 5
4x - 3y = 36, 3x + 4y = 20
2x - 5y = 15, 2x + 5y = 10
Oct 25­8:34 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
parallel, perpendicular, or neither
y = 4x + 3/4, y = (-1/4)x + 4
y = x/3 - 4, y = (1/3)x + 2
y = 5x,
y = -5x + 7
x = 2,
y=9
2x + y = 2 2x + y = 5
4x - 3y = 36, 3x + 4y = 20
2x - 5y = 15, 2x + 5y = 10
Oct 25­8:34 AM
Assignment from Monday
page 594 (9­24)...
Dec 10­8:38 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
page 594 (9­14, 19­24) 16. (8.5, ­9)
18. 89 = 9.4 Dec 10­8:38 AM
Starter: parallel & perpendicular
1. y = 6x + 4 Slope =______________
Parallel line slope=_______
Perpendicular line slope=______
2. Parallel Perpendicular or Neither?
2y + 5x = 12
5y ­ 2x = 12
3. Equation: y = 1/3 x + 6 Find a parallel line through point (3,1)
Find a perpendicular line through pt (3,1)
Nov 10­1:58 PM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
Find the slope of a line that is parallel and
another that is perpendicular to the given line.
Given
y = (1/2)x +2.3
3x + 4y = 12
y=x
7x - y = 5
y=6
y = -3x
2x + 3y = 5
Parallel Slope
1/2
-3/4
1
7
0
-3
-2/3
Perpendicular Slope
-2
4/3
-1
-1/7
undefined
1/3
3/2
Oct 25­8:35 AM
True or False
Two lines with positive slopes can be
perpendicular?False
Two lines with positive slopes can be
parallel? True
Oct 25­8:39 AM
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Math1 distance midpoint parallel perpendicular.notebook
February 20, 2017
HW page 314 # 2­42 even
Oct 14­9:55 AM
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