COORDINATE GEOMETRY
Point on a Plane:
Point of Origin is (0,0)
Points in the xy-plane are represented by two numbers called coordinates:
The first number in the pair is the x-coordinate, which is is the horizontal distance of the point from the origin.Points with positive x-coordinates are on the right of the y-axis and Points with negative x-coordinates are on the left of the y-axis.
The second number is the y-coordinate, which is the vertical distance from the origin.Points with positive y- coordinates are above the x-axis. Points with negative y-coordinates are below the x-axis.
A point is represented by (x, y) where x is called the abscissa and y is called the ordinate.
Distance Between Two Points:
To find the distance between points on a graph by using the distance formula:
2 2
Distance = sqrt((x1 -x2) + (y1 - y2) )
Finding the Slope:
Slope = Change in y/Change in x
= Vertical Rise/Horizontal Run
The slope of the line that contains the points A (2, 3) and B (0, -1) is:
(y2 - y1) / (x2 - x1) = (-1 - 3) / (0 - 2) = -4 / -2 = 2
Slope-Intercept Equation:
Equation to Find the Slope:
To find the slope of a line from an equation, put the equation into the slope-intercept form:
y = mx + b
The slope is m and the y-intercept is b.
To find the slope of the equation 4x + 3y = 4, rearrange it:
4x + 3y = 4
3y = -4x + 4
y = -4/3 x + 4/3
The slope is -4/3
Finding an Intercept:
To find the y-intercept, either:
a)Put the equation into y = mx + b (slope-intercept) form and b is the y-intercept
b)Replace x = 0 into the equation and solve for y.
To find the x-intercept, Replace y = 0 into the equation and solve for x.