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Today
Make-Up Tests? Khan Academy Review Review for Friday’s Test
New Material: Distance & Mid-Point FormulasClass Work
May 14
Warm-Up
Khan Academy: Radical Equations
Khan Academy: Pythagorean Theorem
81 – 26 =
= 7.48
A building is on fire and you need to set the ladder back 10 ft. to prevent burning. What is the shortest ladder (in feet) that will reach the third story window ?
What is the perimeter of the sail?
Test Review: Radical Operations: (4)
The problems on Friday’s test aren’t necessarily more difficult, there are just more types of problems to prepare for. Today and tomorrow, we will review each type.
The Distance Formula:
Class Notes Section of
Notebook
The distance between A and B is
| | | | | | | | | | | | | |
-5 4
A B
| -5 – 4 | = | -9 | = 9
Remember: Distance is always positive
A
B
The Distance Formula Is Derived From The Pythagorean Formula
6
15
6² + 15² = C² = C
As you can see, the shortest distance between two points is...
A straight line; 16.16 < 21
Distance Formula
Dist. = ( x2 - x1 )² + ( y2 - y1 )²
Remember the order ( x , y )
All answers are positive
Find the distance between the two points on the graph.
The Distance Formula:
3,6
8,10 What is the distance
along the x axis?
What is the distance along the y axis?
Let's first use the P.T. to find the distance: a2 + b2 = c2
Dist = ( x - x )² + ( y - y )²
Now, let's use the distance formula....
= 6.4
=
Find the distance between:
( 3 – 8 )² + ( 6 - 10 )²
( -5 )² + ( -4 )²
25 + 16
41 = 6.40
( 8 – 3 )² + ( 10 – 6 )²
( 5 )² + ( 4 )²
25 + 16
41 =6.40
( 3 , 6 ) and ( 8 , 10 )Find the distance between:
( 8 , 10 ) and ( 3 , 6 )
Find the distance between the two points
(3, ) (9, )(x1,y1) (x2, y2)
𝒅=√(𝒙𝟐− 𝒙𝟏)𝟐+(𝒚𝟐−𝒚𝟏)
𝟐
𝒅=√ (𝟗−(𝟑))𝟐+(−𝟒−𝟒)𝟐
𝒅=√ (𝟔 )𝟐+(−𝟖)𝟐𝒅=√𝟏𝟎𝟎
𝒅=𝟏𝟎
Find the distance of the line.1. (, 1) (, 3)
(x1, y1)
(x2, y2)
𝒅=√(𝒙𝟐− 𝒙𝟏)𝟐+(𝒚𝟐−𝒚𝟏)
𝟐
𝒅=√(−𝟐− (−𝟒 ))𝟐+(𝟑−𝟏)𝟐
𝒅=√ (𝟐 )𝟐+(𝟐)𝟐
𝒅=𝟐√𝟐
𝒅=√𝟒+𝟒
𝒅=√𝟖𝒅=√𝟐 ∙𝟒
Find the distance between:
The Distance Formula:
Class Work:
See
Handout
Review Graphingy
x
( 0,0 )Origin
Positive
Negative
Order ( X,Y )Quadrant
IQuadrant
II
QuadrantIII
QuadrantIV