GMAT® Official Guide 2019 Quantitative Review
Each point in the plane has an x-coordinate and a y-coordinate. A point is identified by an ordered pair
(x,y) of numbers in which the x-coordinate is the first number and they-coordinate is the second number.y
5
4(^3) •P
2
1
-5 -4 -3 -2 -1 O 1 2 3 4 5 X
I -1
-2
Q .... - -3
-4
-5
In the graph above, the (x,y) coordinates of point Pare (2,3) since Pis 2 units to the right of the y-axis
(that is, x = 2) and 3 units above the x-axis (that is,y = 3). Similarly, the (x,y) coordinates of point Qare
(-4,-3). The origin O has coordinates (0,0).
One way to find the distance between two points in the coordinate plane is to use the Pythagorean
theorem.
(-2,4)
R
I
I
y
z•- - - - s
(3,-3)
To find the distance between points Rand S using the Pythagorean theorem, draw the triangle as
shown. Note that Z has (x,y) coordinates (-2,-3), RZ = 7, and ZS= 5. Therefore, the distance between
R and S is equal to
✓ 72 + 52 = ffe.
For a line in the coordinate plane, the coordinates of each point on the line satisfy a linear equation of
the form y = mx + b (or the form x = a if the line is vertical). For example, each point on the line on the
next page satisfies the equation y =-lx+l. One can verify this for the points (-2,2), (2,0), and (0,1)
2
by substituting the respective coordinates for x and y in the equation.