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.
  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 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

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
2 Quadratic Equations
3 Set Theory
4 Sequences & Series
5 Number Properties & Theory
6 Inequalities
7 Functions

Math Lesson Book 2


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

Math Lesson Book 3


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