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### Concepts Tested from Coordinate Geometry in GRE

Length of a line segment joining two points, coordinates of a point P that lies on a line segment and divides the line segment in a given ratio, computing the slope of a line if the coordinates of two points through which the line passes is known, testing for collinearity of three or more points, finding the equation of a line and that of parallel and perpendicular lines, computing coordinates of centroid, orthocenter and circumcenter of a triangle, finding equations of median, perpendicular bisector, altitude and angle bisector of a triangle coordinates of whose vertices are known, finding radius of a circumscribing circle, equations of circles, and distance between a point and a line.

A straight line 4x + 3y = 24 forms a triangle with the coordinate axes. What is the distance between the orthocentre of the triangle and the centre of the circle that circumscribes the triangle?

- 10 units
- 5 units
- 13 units
- 12 units
- 9 units

GRE Quantitative Comparison Question

Quantity A Quantity B Length of the segment of the line 4x + 3y = 12 intercepted between the coordinate axes. Length of the median to side BC of triangle whose coordinates are A(4, 4), B(7, 4) and C(4, 8) - Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given