Difference between revisions of "Coordinate system"
| Line 1: | Line 1: | ||
| − | The coordinate system is often used in geometry. The cordinate system is organized to 4 quadrants. In the first quadrant, both (x,y) are positive. In the second quadrant x is negative, while y is positive.In the third quadrant, both (x,y) are negative. Finally, in the fourth quadrant x is positive while y is negative. To find the slope of a line on the coordinate system with points <math>(x_1, y_1); (x_2, y_2)</math> we need to compute <math>\frac{y_2-y_1}{x_2-y_2}</math>. The slope is usually expressed as <math>m</math>. Also, there is the point-slope form which states <math>y=m \cdot x + b</math> for some real numbers b,x,y. Also, if two lines are perpendicular, then product of the slopes is -1. (For example, the slope could be -3/4 and 4/3.) The coordinate system is also widely useful were right triangle, since there is 90 degrees. | + | The coordinate system is often used in geometry. The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers, (x,y). The cordinate system is organized to 4 quadrants. In the first quadrant, both (x,y) are positive. In the second quadrant x is negative, while y is positive.In the third quadrant, both (x,y) are negative. Finally, in the fourth quadrant x is positive while y is negative. To find the slope of a line on the coordinate system with points <math>(x_1, y_1); (x_2, y_2)</math> we need to compute <math>\frac{y_2-y_1}{x_2-y_2}</math>. The slope is usually expressed as <math>m</math>. Also, there is the point-slope form which states <math>y=m \cdot x + b</math> for some real numbers b,x,y. Also, if two lines are perpendicular, then product of the slopes is -1. (For example, the slope could be -3/4 and 4/3.) The coordinate system is also widely useful were right triangle, since there is 90 degrees. |
Revision as of 00:20, 25 January 2016
The coordinate system is often used in geometry. The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers, (x,y). The cordinate system is organized to 4 quadrants. In the first quadrant, both (x,y) are positive. In the second quadrant x is negative, while y is positive.In the third quadrant, both (x,y) are negative. Finally, in the fourth quadrant x is positive while y is negative. To find the slope of a line on the coordinate system with points 
we need to compute 
. The slope is usually expressed as 
. Also, there is the point-slope form which states 
for some real numbers b,x,y. Also, if two lines are perpendicular, then product of the slopes is -1. (For example, the slope could be -3/4 and 4/3.) The coordinate system is also widely useful were right triangle, since there is 90 degrees.
