# Introduction

On a number line, the numbers increase in size to the right and decrease to the left:

â€‹

If we draw a line through the point 0 perpendicular to the number line, we will form a grid:

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The thick horizontal line in the above diagram is called the

*x*-axis, and the thick vertical line is called the*y*-axis. The point at which the axes meet, (0, 0), is called the origin. On the*x*-axis, positive numbers are to the right of the origin and increase in size to the right; further, negative numbers are to the left of the origin and decrease in size to the left. On the*y*-axis, positive numbers are above the origin and ascend in size; further, negative numbers are below the origin and descend in size. As shown in the diagram, the point represented by the ordered pair (*x, y*) is reached by moving*x*units along the*x*-axis from the origin and then moving*y*units vertically. In the ordered pair (*x, y*),*x*is called the*abscissa*and*y*is called the*ordinate*; collectively they are called coordinates. The*x*and*y*axes divide the plane into four quadrants, numbered I, II, III, and IV counterclockwise.

**Note:**if

*x*â‰

*y*, then (

*x, y*) and (

*y, x*) represent different points on the coordinate system. The points (2, 3), (â€“3, 1), (â€“4, â€“4), and (4, â€“2) are plotted in the following coordinate system:

Example

In the figure, polygon

*ABCO*is a square. If the coordinates of*B*are (*h*, 4), what is the value of*h*?- 4
- -4
- not enough information

Solution

Since the
Since figure
Since point
Be careful not to choose 4.

*y*-coordinate of point*B*is 4, line segment*CO*has length 4.*ABCO*is a square, line segment*AO*also has length 4.*B*is in the second quadrant, the*x*-coordinate of*B*is â€“4. The answer is (D).*h*is the*x*-coordinate of point*B*, not the length of the squareâ€™s side.