the coordinate plane section 1.6. goal - after today, you will be able to: find the distance...

The Coordinate PlaneSection 1.6

Goal - After today, you will be able to:

Find the distance between any two points in the coordinate plane.

Find the coordinates of the midpoint of a segment in the coordinate plane.

The Coordinate PlaneThe Cartesian Plane

The X-Y Plane

The Coordinate PlaneThe Cartesian Plane

The X-Y Plane

Logan Square (Circle) Franklin Square

Rittenhouse Square Washington Square

Finding Distance

If two points in the coordinate plane lie on a vertical or horizontal line, you can use the Ruler Postulate to find the distance between them.

If two points do NOT lie on a vertical or horizontal line, you need to use the Distance Formula or Pythagoreans Thm.

The Distance FormulaThe Distance Formula

The main thing to watch out for isCorrectly labeling the points. Then you

Just “plug and chug”

A( 2,1)

B(5,2)

Calculate the distance between the two points:

•A(1,2) B(3,7)

•C( -2,4) D(3,-6)

•E(-1,-5) F(-6, -8)

Find:DE =

FG =

RS =

(0 4)2 ( 2 0)2 16 4

20 2 5 4.47

(4 2)2 ( 1 3)2 4 16

20 2 5 4.47

(2 3)2 ( 2 4)2 25 4

29 5.38

The Midpoint FormulaThe Midpoint Formula

Remember, You are finding A POINT!So, your answer Needs to have BOTH coordinates

Label points just as we did for distanceFormula, and plug ‘em in!

Calculate the midpoint between the two points:

•A(1,2) B(3,7)

•C( -2,4) D(3,-6)

•E(-1,-5) F(-6, -8)

midpt is x1 x2

2,y1 y2

2

B(0,4)

C(5,4)

D(-1,-2)

E(-4,0)

F(1,-2)

A(-3,2)

G(3,0)

Section 1.7 - Review ofPerimeter, Circumference, & Area

For Rectangles, Triangles, and Circles

Perimeter - “Sum of Side Lengths”

Area of Rectangle - “Base times Height”

Area of Triangle - “1/2 Base times Height”

Find the Area and Perimeter.

Find the Area and Perimeter.

Circle Circumference and AreaFor Circles with Radius r

Circumference =

Area =

r2

2r

Before we work with circles, we have to answerA few questions.1. What is radius vs diameter2. What is π3. What is the difference between A & C

Radius v. Diameter Area v. Circumference

The London Eye

What is Pi?

Pi

Finding Area and Circumference of Circles.

What does it mean to “leave your answer in terms of π”

r = A =

C =

r = A =

C =

Classwork / HomeworkPage 46 - 3, 6, 13, 20, 24*, 28*,31, 42

53-56 on graph paper

Page 55 - 1, 3, 6, 7, 9, 16, 20 28, 37, 38, 50, 65

Chapter 1 reviewPage 61-64 – Whichever problems you choose to do…