C oordinate 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.

### Concepts Covered

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:

- The Cartesian plane - abscissa and ordinate
- Reflection of a point and polar coordinates
- Detailed explanation of the concepts in points and line segments - distance between points, midpoint theorem
- Slope of line, ratio in which a point on a line segement divides the line segment
- Centroid and area of a triangle given the coordinates of the verticles of a triangle
- Point on a locus, shifting of origin and the relationship between the straight lines and linear equations
- Lines - Equation of a line (point slope formula, two point formula)
- Computing slope of a line and intercepts of a line from the equation of a line.
- Slope of parallel lines and perpendicular lines
- Distance between two lines and angle between the two lines
- Circles and their equation - center and radius
- 7 illustrative examples and 23 solved examples to consolidate the concepts covered.
- 12 exercise problems with the answer key and explanatory answers
- 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 from this chapter.

### Sample Question

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

- I and III only
- I, II and III only
- II, III and IV only
- II and IV only
- 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.

##### 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).

Practice Questions - Coordinate Geometry Buy Wizako's Math Books

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

1 | Linear Equations | Details |

2 | Quadratic Equations | Details |

3 | Set Theory | Details |

4 | Sequences & Series | Details |

5 | Number Properties & Theory | Details |

6 | Inequalities | Details |

7 | Functions |