The horizontal number line is called the x-axis, and the vertical number line is called the y-axis in rectangular coordinate system which intersect at a right angle, first number is x-coordinate and second number is y-coordinate. The two number lines define a flat surface is called a plane, and each point on this plane is associated with an ordered pair of real numbers (x, y) with origin point (0, 0).
The rectangular coordinate system is the uniquely identify points in a plane using ordered pairs (x, y) that indicate position relative to the origin. The x-coordinate is the position from left and right of the origin on horizontal line and y-coordinate is the position above or below the origin on vertical line.
The coordinate plane: plotting points and finding their coordinates
The four quadrants and the coordinates they contain:
- Quadrant I include every point with a positive x-coordinate and a positive y-coordinate.
- Quadrant II include every point with a negative x-coordinate and a positive y-coordinate.
- Quadrant III include every point with a negative x-coordinate and a negative y-coordinate.
- Quadrant IV include every point with a positive x-coordinate and a negative y-coordinate.
Finding a midpoint: given two points, which point is exactly halfway between? To find a midpoint, take the average of the x-coordinates and the average of the y-coordinates.
Graphs are used to visualize real-world data which independent data is associated with x-coordinates and dependent data is associated with y-coordinates.
Pythagorean theorem provide a necessary and sufficient condition of right triangles that measures of the sides by a^2+b^2=c^2.
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