Analyzing Polygons with Coordinates
Click below for
In a coordinate plane, there are four quadrants.
Quadrant I is positive, the x-coordinates are positive and the coordinates are positive.
Quadrant II is negative, the x-coordinates are negative and the y-coordinates are positive.
Quadrant III is positive, the x-coordinates are negative and the y-coordinates are negative.
Quadrant IV is negative, the x-coordinates are positive and the y-coordinates are negative.
If a slope is positive, then the line segment representing the slope begins in Quadrant III and ends in Quadrant I. If the slope is negative, then the line segment representing the slope begins in Quadrant II and ends in Quadrant IV.
You can think of it this way. We read from left to right. If we are reading and the slope goes up, then the slope is positive. If we are reading and the slope goes down, then the slope is negative.
A line with a zero slope is a horizontal line. An equation of a line with zero slope is y = 2.
The following table shows the coordinates of a horizontal line. ("n" is any real number).
A line with an undefined slope is a vertical line. An equation of a line with an undefined slope is
x = 2
To graph quadrilaterals or other polygons on a coordinate plane, graph the coordinate points, then connect the points.
The terms rise and run are used to define slope. Slope is sometimes defines as rise over run (rise/run) The rise is the y coordinates and the run is the x coordinates. Rise goes up, run is horizontal.
Suppose that non vertical lines p and q are perpendicular and tha the slope of p is m. What is the slope of q? According to the perpendicular lines theorem, the product of their slopes is -1. Therefore pq = -1. If p is m, then q must be the negative reciprocal of m or -1/m.
All horizontal lines are perpendicular to all vertical lines.
Real life situations that involve slope include, roofing a house, the grade of a road on a hill, ramps for disabled people, ramps used for loading and unloading material, building staircases, takeoffs and landings of airplanes, etc.