## Sunday, November 8, 2009

### GMAT/CAT PREPARATION EMAIL COURSE DAY 21

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.