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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