Coordinate Geometry Book
Table of Contents
- Distance
- Distance
- Distance Practice
- Distance SOLUTION
- Midpoint
- midpoint
- Midpoint Practice
- Midpoint SOLUTION
- Slope
- Slope
- Slope Practice and Solution
- Slope-Intercept Form
- Slope-Intercept Form
- Slope-Intercept Practice
- Slope-Intercept SOLUTION
- Standard Form
- Standard Form
- Standard Form Practice and Solutions
- Area
- Area
- Area Practice
- Area SOLUTION
- Perimeter
- Perimeter
- Perimeter Practice
- Perimeter SOLUTION
Distance
Let's say that Point A is Chipotle, and Karl and Kyle both have to walk to their houses from Chipotle. If Karl goes two blocks West and 5 blocks South to his house, and Kyle goes two blocks east from Chipotle and 5 blocks North, how far apart are the two houses? Well to find out, you have to use the distance formula: [math]_{ }\surd\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2[/math] So plug in the two coordinates of the houses (Point E and Point C). When you are done, you should end up with the answer of 10.8 blocks.
midpoint
The midpoint can be found by using the formula of x1+x2/2 and y1+y2/2 which gives you the midpoint coordinates.
For example, if the coordinates of A are (-2, 5) and the coordinates of B are (2, 3), then you would simple do -2+2/2 to get the x coordinate of the midpoint, and the same thing for the y coordinate which would be 5+3/2. The coordinate of the midpoint would then be (0, 4)
Slope
Slope is used to describe the angle at which a line is positioned. Slope can be called "m" and is seen in the slope-intercept formula y=[b]m[/b]x+b. Slope is the [math]\frac{Rise}{Run}[/math] ; rise is the difference in the y value of two points on the line and run is the difference in the x value of two points on the line. The formula for slope is [math]\frac{y_2-y_1}{x_2-x_1}[/math]where the two points that are on the line are [math]\left(x_1,y_1\right)[/math] and [math]\left(x_2,y_2\right)[/math]
Slope-Intercept Form
Slope-intercept form is y=mx+b. The slope of the line (rise/run) is represented by "m". The y-intercept is represented by b; this is where the line crosses the y-axis. Slope-Intercept Form is the most common and easiest way to describe a line on the coordinate plane.
Standard Form
Standard form is another way to describe a line. The basic equation for standard form is ax+by=c. The values a,b, and c are all whole numbers that give the line its properties. "A" should always be positive, "a" and "b" can not be 0. To change a line that is in slope-intercept form (y=mx+b) to standard form you need to perform inverse operations. Subtract "mx" from both sides of the equation. Now you should have "-mx+y=b". Next you will need to make sure that "m" (a) is positive. You will multiply the entire equation by -1 and you will get "mx-y=-b". If applicable make any fractions whole numbers by multiplying the entire equation by the denominator. Now your equation is in standard form! Go to the next worksheet for some practice.
Area
Perimeter
To find the distance of BC, you will have to do the distance formula which is [math]\surd\left(x^1-x^2\right)^2+\left(y^1-y^2\right)^2[/math] to get the distance of 5.39 units.