You will get two to three questions from Coordinate Geometry in the GMAT quant section. Questions appear in both variants viz., problem solving and data sufficiency. The concepts tested include finding the slope, identifying the quadrants through which a line passes, finding the length of a line segment, determining the equation of a line, equations of parallel and perpendicular lines, area of triangle, and equation of circles. Sample GMAT practice questions in coordinate geometry is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

What is the equation of a circle of radius 6 units centered at (3, 2)?

- x
^{2}+ y^{2}+ 6x - 4y = 23 - x
^{2}+ y^{2}- 6x + 4y = 23 - x
^{2}+ y^{2}+ 6x + 4y = 23 - x
^{2}+ y^{2}- 6x - 4y = -23 - x
^{2}+ y^{2}- 6x - 4y = 23

- x
Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (8, 0) and the point (0, 12) is the lowest among all elements in set S. How many such points P exist in set S?

- 1
- 5
- 11
- 8
- 3

__Data Sufficiency__: Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at (p, q).

Is p + q > 0?- x intercept of Line L is less than that of Line K
- y intercept of Line L is less than that of Line K

__Data Sufficiency__: Does the line x + y = 6 intersect or touch the circle C with radius 5 units?- Center of the circle lies in the third quadrant.
- Point (-4, -4) does not lie inside the circle.

__Data Sufficiency__: Is the slope of the line that passes through the point (p, q) positive?- p, q > 0
- The x-intercept of the line is k, such that k > p.

### Video Explanation

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