1. Geometry 1-6 and 1-7 Notes
August 22, 2016 or
August 23, 2016

2. 1-6 The Coordinate Plane Learning Objectives
Find the distance between two points on the coordinate plane
Find the midpoint of a segment on the coordinate plane
If two points are on a horizontal or vertical line, we can count to find the distance between (or use the ruler postulate)
The distance is 2 units

3. 1-6 The Coordinate Plane
You can describe a point by an ordered pair (x,y)
Called the coordinates of the point
When two points are not on a horizontal or vertical line, we need to use the coordinates (x1,y1) (x2,y2)
Point A has coordinates (x1,y1). We will use this as our first point (1,1) so x=1 and y=1
Point B has coordinates (x2,y2)=(3,3) so x=3 and y=3
B (3,3) d
A (1,1)

4. 1-6 The Coordinate Plane The Distance Formula Example
The distance d between two points A (x1,y1) and B (x2,y2) is:
Example
Find the distance between A(1,1) and B(3,3)
x1= 1, y1= 1 and x2 = 3, y2 = 3
𝑑= (3−1) 2 + (3−1) 2
𝑑= (2) 2 + (2) 2
𝑑= 4+4
𝑑= = 2.8 (rounded)

5. 1-6 The Coordinate Plane The Distance Formula Example
The distance d between two points A (x1,y1) and B (x2,y2) is:
Example
Find the distance between R(-1,4) and S(2,3)
x1= -1, y1= 4 and x2 = 2, y2 = 3
𝑑= (2−(−1) 2 + (3−4) 2
𝑑= (3) 2 + (−1) 2
𝑑= 9+1
𝑑= = 3.2

6. 1-6 The Coordinate Plane
To find the midpoint, find the average of the endpoints coordinates. Our midpoint has an x-value that is halfway between the x’s and a y-value that is halfway between the y’s.
Midpoint Formula
The coordinates of the midpoint M of 𝐴𝐵 with endpoints A (x1,y1) and B (x2,y2) are the following:
𝑀=( x1+ x2 2 , y1 + y2 2 )

7. 1-6 The Coordinate Plane 𝑀=( x1+ x2 2 , y1 + y2 2 ) Example
𝐴𝐵 has endpoints A(3,5) and B(0,-3). Find the coordinates of its midpoint M.
A (3,5) (x1,y1)
B (0,-3)(x2,y2)
𝑀=( , 5 + −3 2 )
𝑀=( 3 2 , 2 2 )
𝑀= (1 1 2 ,1) A M B

8. 1-7 Perimeter, Circumference, and Area
Learning Objectives
Find perimeter and circumference
Find area of rectangles, circles, and irregular shapes
Understand and use Postulates 1-9 and 1-10
Perimeter – is the distance around a figure
Area – is the space inside a figure
Perimeter = h + b + h + b or P = 2h + 2b
P = 2(2cm) + 2(5cm) = 14cm
Area = bh
A = (2cm)(5cm) = 10cm b
5cm h h
2cm b

9. 1-7 Perimeter, Circumference, and Area
Squares
Squares are rectangles with the same side length, s
Perimeter: P = 4s
Area: A = 𝑠 2
Circles
Circumference: C = 𝜋𝑑 or C = 2𝜋r
Area: A = 𝜋 𝑟 2
𝜋 is irrational and goes on forever so we can never have an exact answer with 𝜋.
For an approximate answer, use 𝜋 = 3.14
For a rounded answer, use the 𝜋 on your calculator
For an exact answer, leave 𝜋 in the answer D S R S S
Radius = r
Diameter = d S

10. 1-7 Perimeter, Circumference, and Area
Example
Find the circumference
C = 𝜋𝑑
C = 3𝜋 use this for an exact answer
C ≈ = 9.42 use this for an approximate
C = 3·𝜋 in calculator = ≈ 9.42 rounded 3m

11. 1-7 Perimeter, Circumference, and Area
Example: Finding Perimeter in the Coordinate Plane
Find the perimeter of ABC with points A(-3,-1), B(2,-1), C(2,5)
First: Sketch out shape
AB = 2−(−3) = 5
BC = 5− −1 =6
𝐴𝐶= (2−(−3)) 2 + (5−(−1)) 2 = =
= ≈ 7.8
AB + BC + AC = = 18.8 units
Perimeter of ABC is 18.8 units
C (2,5)
Use the Ruler Postulate
Use the Distant Formula
A (-3,-1)
B (2,-1)

12. 1-7 Perimeter, Circumference, and Area
Postulate 1-9
If two figures are congruent, then their areas are equal
Postulate 1-10
The area of a region is the sum of the areas of its non-overlapping parts
*Postulate 1-10 tell us that to find the area of an irregular shape, we just need to break it into shapes we can find the area of, these shapes we can find the area of, if added together, will equal the irregular shape.

13. Homework
1-6 pg. 46 #1-6, 11, 12, even, 37, 38, 53, pg. 55 #1, 3, 6, 7, 10, 11, 14-16, 20, 24, 28, 29, 32, 39, 40, 50, 59, 70