GRE® Coordinate Geometry

Problem solving, More Than One Answer, and Comparison

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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.

  1. 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?

    1. 10 units
    2. 5 units
    3. 13 units
    4. 12 units
    5. 9 units
  2. 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)
    1. Quantity A is greater
    2. Quantity B is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given

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