# GMAT Book 3: Coordinate Geometry

#### GMAT Quant Review | XY coordinates, lines, circles, equations

Coordinate goemetry is a must learn topic and usually gets tested in the GMAT Quant section. Questions in the GMAT from this topic appear in both variants viz., problem solving and data sufficiency.

## Syllabus Covered in Wizako's GMAT Book | Coordinate Geometry

Basics of coordinate geometry (co-geo) including concepts of slopes, intercepts, and quadrants, are often tested 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. Wizako'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, section formula, and midpoint formula.
4. Slope of line, ratio in which a point on a line segement divides the line segment.
5. Centroid and area of a triangle given the coordinates of the verticles of a triangle.
6. Point on a locus, shifting of origin and the relationship between the straight lines and linear equations.
7. Lines - Equation of a line (point slope formula, two point formula).
8. Computing slope of a line and intercepts of a line from the equation of a line.
9. Slope of parallel lines and perpendicular lines.
10. Distance between two lines and angle between the two lines.
11. Circles and their equation - center and radius.
12. 7 illustrative examples and 23 solved examples to consolidate the concepts covered.
13. 12 exercise problems with the answer key and explanatory answers.
14. A multiple choice test with 33 GMAT level questions in the work book. Answer key and explanatory answers are provided for all questions.

Here is a typical solved example in Wizako's GMAT Book from this chapter

### Sample 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

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.

#### Applying the concept in this question

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).

### More in GMAT Coordinate Geometry

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