Using a Cartesian plane (see image), you can plot points (x,y).
To find the distance between two points, use the "Distance Formula"(See table)
To find the mid-point between two coordinates on a line, use the "Midpoint Formula" (See table)
LINEAR EQUATIONS AND GRAPHS
To show points on a Cartesian plane, use variables x and y (or any variable) and multiples of the variables to create a linear.
For example, y = 2x + 6, follows the most common linear relationship. The variable "m" is the gradient (slope), and "c" is the y-intercept.
The gradient of a line can be found using the equation
*Note: If two lines have the same gradient, they are parallel; if they have opposite reciprocal gradients, the lines are perpendicular.
Cartesian Plane |
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Distance Formula |
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Midpoint Formula |
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SIMULTANEOUS EQUATIONS
The elimination method is used in solving equations with the same variables. One variable is eliminated so that the other may solved in either equation.
For example, in the equation:
x - 2y = 7
2x + 3y = 0
The top equation is multiplied by 2 to cancel out the x variables and y is then found to be 2.
Substitution is used when one variable is eliminated so that the other may be added or subtracted. The initial variable is then solved by substituting in the solved variable.
For example, in the equation:
x - 2y = 7
2x + 3y = 0
The top equation is multiplied by 2 to cancel out the x variables and y is found to be 2. When this y-value is placed in the original bottom equation, x is found to be -3.
The graphical method is the last method that can be used in solving simultaneous equations. The intersection of the two lines on a graph are there solution, though this can often give only an approximate answer.
APPLICATIONS OF COORDINATE GEOMETRY
Coordinate geometry is useful when finding coordinates, areas, slopes, angles and gradients of lines and the shapes they make. Basically, it helps the mathematician visualize the object made by points.
COORDINATE GEOMETRY IN 3-D
Coordinate geometry is not only used in 2-D form. In 3-D form the position of points is places on three perpendicular planes ranging from the origin (point O). These planes are labeled x,y and z and are written in the order: (x-value, y-value, z-value).
When you plot these points you create the vertices of a 3-D shape.
Much like in a 2-D plane, the distances and midpoints can be found using slightly modified formulas.
Distance = the square root of[(x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2]
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)
Robinson IB Program
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Fun coordinate geometry images!
Edhelper
Hope you learned lots about Coordinate geometry!