 # Book 3: Coordinate Geometry

XY coordinates, lines, circles, equations

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:

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
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.
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 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

##### 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).

### 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

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details