SS Geometry Project
We will make math great again. We are with Math. Math trumps hate. It is true, just fantastic, look at science, english, it's a disaster, an EPIC fail, this math, it's gonna be huge, it's gonna be great.
Table of Contents
- Distance
- Distance
- Midpoint
- Midpoint
- Slope
- Slope
- Slope-Intercept Form
- Slope-Intercept Form
- Standard Form
- Standard Form
- Area
- Area
- Perimeter
- Perimeter
Distance
[size=200][quote]Distance is the length of units between two specific points. You find distance by using the following formula:[/quote][/size]
Distance Formula
This is an example of how you would use the distance formula to find the distance from the points (1,1), and (1,5).[br][math]\left(1,1\right),\left(1,5\right)->\sqrt{\left(1-1\right)\begin{matrix}^2\end{matrix}+\left(5-1\right)^2}=4[/math]
What is the Distance between point (1,2) and point (-1, -2)?
Create a line segment, using the the point tools, create two points, an then join them using the line segment tool. Use the distance tool, clicking point A first, and then point B second. (The titles of the dots will appear once the distance shows up. It does not matter the order you click the points.)
Midpoint
What is a midpoint?
A point that is halfway between points A and B.
This is an example of the midpoint formula.
Example:
What is the midpoint of the line segment AB? Use the Midpoint Formula above.
Line Segment AB
Slope
[size=200][quote]Slope is the measure of how steep a line is. A line that moves up from left to right, has a positive slope, and a line that goes the other way has a negative slope.[/quote][/size]
Slope Formula
If a line has points at (1,2) and at (0, -1), what is it's slope? Use graph below to help you solve the question, and remember the formula shown at the beginning of this worksheet, it will give you the formula for slope.
Graph for above question:
Slope-Intercept Form
What is Slope-Intercept Form?
Slope-Intercept Form is a way to write the equation of a line so that the slope and y-intercept are immediately clear.
This image shows the Slope-Intercept Form, and an example of what the variables represent.
What does the variable "m" in the equation y=mx+b represent?
What does the variable "b" represent in the equation y=mx+b?
What is the slope of the line, y=3x+5?
What is the y-intercept of the line, y=2x+6?
Standard Form
[size=200][quote]Standard Form is a way of describing a line in the format of Ax+By=C, where it can easily be translated to y=mx+b form.[/quote][/size]
[color=#ff0000]In y=mx+b form, this line is y=x, the most simple line one can have. But in Standard Form, which is Ax+By=C, it is written as -1x+1y=0.[/color]
Going from Ax+By=C to y=mx+b
[color=#0000ff]To go from Ax+By=C to y=mx+b, you must follow these steps.[br][br]First, we'll use 2x+2y=2 as our example. [br]1. Subtract 2x from both sides, to get 2y=2x+2. You cannot combine 2 with 2x.[br]2. Divide both sides by 2, from the 2y. (2x/2 = x), (2/2 = 1), if you put these two together, you will get y=x+1.[br]3. Answer = y=x+1[/color]
Describe how Standard Form differs from Y=mx+b form.
Area
What is Area?
Area is the extent or measurement of a surface or 2-dimensional object.
This is the area formula for finding the area of a parallelogram or rectangle.
BC is the base, DC is the height, so if the formula is bxh=area, then the 8x6=area and the Area of ABCD is 48.
Let's say that b=6 and h=2. What would be the area of that figure?
Area of a Triangle
The formula for finding the area of a triangle is (bxh)/2=area.
Let's say now the base of the triangle is 5 and the height is 10, What is the area of the triangle now?
Perimeter
[size=150][size=200][quote]Perimeter measures the length of all the sides put together of a shape.[/quote][/size][/size]
The Formula for perimeter is P = a+b+c+......... however many sides you need. The alphabet runs out at 26, but you can start making symbols up if your shape has more than that many sides. For now, stick to the square.
[br][color=#ff0000][size=150]So, the perimeter of this object is P = 10+10+10+10=40, which, in this specific case, could be written as P=(4(10))=40[/size][/color]
In the below image, what is the Perimeter of the object?