Today

Make-Up Tests?

Review For Final Exam

Review Pythagorean Theorem

New Material: Distance Formula

Class Work 4.10

May 13

2

x2 – x + 2 = 0

(x – 2)(x + 1) Solutions are: x = 2, x = -1

Extraneous Solution is x = -1

Final Exam Review:

Add, Subtract, Multiply, & Divide 𝟑𝟖

and 𝟕𝟗. Reduce to its simplest terms.

a. 𝟑

𝟖+ 𝟕𝟗

= 𝟑

𝟖+ 𝟕𝟗

= 𝟖𝟑𝟕𝟐

= b. 𝟑

𝟖- 𝟕

𝟗= 𝟐𝟕−𝟓𝟔

𝟕𝟐= - 𝟐𝟗

𝟕𝟐

c. 𝟑

𝟖•𝟕

𝟗= 𝟐𝟏

𝟕𝟐= 𝟕

𝟐𝟒d.

𝟑

𝟖÷ 𝟕

𝟗= 𝟑

𝟖•𝟗

𝟕= 𝟐𝟕

𝟓𝟔=

1𝟏𝟏𝟕𝟐

Pythagorean Theorem

81 – 26 = 𝟓𝟔 = 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?

9' + 12' + 15' = 36'

2 𝟏𝟒

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

𝟐𝟔𝟏 = 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:

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

Now, let's use the distance formula....

52 + 42 = 412

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 )

When Using the distance formula, it does not matter what

point is used for x1 and x2. Be sure your y1 is from the same

coordinate pair as the x1

Find the distance between the two points

(x1,y1) (x2, y2)

Find the distance of the line.

(x1, y1) (x2, y2)

Find the distance between:

12 − 6 + (3 5 2 5)2 2 = 45 – 30 – 30 + 20

The Distance Formula

There are two different types of problems to solve withe the distance formula.

A. All four of the coordinates are known. Solve for the distance.B. Three of four coordinates and the distance is known. Solve for the fourth coordinate.

Example 1. Find the distance between the two points.

(-2,5) and (3,-1)

• Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)

A. All four of the coordinates are known. Solve for the distance.

Example 2.

B. Three of four coordinates and the distance is known. Solve for the fourth coordinate.

B. Three of four coordinates and the distance is known. Solve for the fourth coordinate.

Class Work: 4.10

Review Graphingy

x

( 0,0 )

Origin

Positive

Negative

Order ( X,Y )Quadrant

I

Quadrant

II

Quadrant

III

Quadrant

IV

Khan Academy: Radical Equations