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Concepts Covered
Basics of coordinate geometry (co-geo) including concepts of slopes, intercepts, and quadrants, are often repeated questions both in the GMAT Problems Solving section and in the GMAT Data Sufficiency section of the GMAT Math Section. A good grasp of the fundamentals of co-geo will help you crack questions from this topic with relative ease. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts:

1. The Cartesian plane - abscissa and ordinate
2. Reflection of a point and polar coordinates
3. Detailed explanation of the concepts in points and line segments - distance between points, midpoint theorem etc
4. Centroid, incenter and area of a triangle given the coordinates of the points
5. Point on a locus, shifting of origin and the relationship between the straight lines and linear equations
6. Lines - Equation of a line (point slope formula, two point formula), slope of a line, and intercepts
7. Slope of parallel lines and perpendicular lines
8. Distance between two lines and angle between the two lines
9. Circles and their equation - center and radius
10. 24 solved examples with illustrations
11. 12 exercise problems with the answer key and explanatory answers

Here is an example of a typical solved example in this chapter.

Question
The straight line represented by the equation 3x - y = 12 passes through the following quadrants

1. I and III only
2. I, II and III only
3. II, III and IV only
4. II and IV only
5. I, III and IV only

Explanatory Answer
Concept Note
A positive sloping line passes through the I and the III quadrant.
If the positive sloping line intercepts the Y-axis on the positive side, the line passes through I, III and II quadrant. If the positive sloping line intercepts the Y-axis on the negative side, the line passes through I, III and IV quadrant.

A negative sloping line passes through II and IV quadrant.
If the negative sloping line intercepts the Y-axis on the positive side, the line passes through II, IV and I quadrant. If the negative sloping line intercepts the Y-axis on the negative side, the line passes through II, IV and III quadrant.

Rewriting the given equation in the standard y = mx + c, we get y = 3x - 12.
The slope of the line is 3, which is positive

Therefore, the line passes through the I and III quadrant.

The Y-intercept is negative. So, the line passes through I, III and IV quadrant.

The correct answer is choice (E).