Tài liệu Master the Gre 2010 - Part 32 pdf

y-coordinate is its vertical position on the plane. You denote the coordinates of a point

with (x,y), where x is the point’s x-coordinate and y is the point’s y-coordinate.

The center of the coordinate plane—the intersection of the x- and y-axes—is called the

origin. The coordinates of the origin are (0,0). Any point along the x-axis has a

y-coordinate of 0 (x,0), and any point along the y-axis has an x-coordinate of 0 (0,y).

The coordinate signs (positive or negative) of points lying in the four Quadrants I–IV

in this next figure are as follows:

Notice that we’ve plotted three different points on this plane. Each point has its own

unique coordinates. (Before you continue, make sure you understand why each point

is identified by two coordinates.)

Defining a Line on the XY-Plane

You can define any line on the coordinate plane by the equation:

y 5 mx 1 b

In this equation:

• The variable m is the slope of the line.

• The variable b is the line’s y-intercept (where the line crosses the y-axis).

• The variables x and y are the coordinates of any point on the line. Any (x,y) pair

defining a point on the line can substitute for the variables x and y.

Determining a line’s slope is often crucial to solving GRE coordinate geometry

problems. Think of the slope of a line as a fraction in which the numerator indicates

the vertical change from one point to another on the line (moving left to right)

corresponding to a given horizontal change, which the fraction’s denominator indi￾cates. The common term used for this fraction is “rise over run.”

You can determine the slope of a line from any two pairs of (x,y) coordinates. In

general, if (x1,y1) and (x2,y2) lie on the same line, calculate the line’s slope as follows

(notice that you can subtract either pair from the other):

Chapter 11: Math Review: Geometry 293

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