GRE® Coordinate Geometry

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Concepts Tested from Coordinate Geometry in the 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
    Choice B
    5 units
    Approach to solve this Coordinate Geometry Question

    Step 1: Compute the coordinates of the Triangle.
    Step 2: Determine the coordinates of the orthocentre.
    Step 3: Determine the coordinates of the circumcentre.
    Step 4: Compute the length of the line segment.

  2. Quantitative Comparison

    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(10, 4) and C(4, 12)

    1. Quantity A is greater
    2. Quantity B is greater
    3. The two quantities are equal
    4. Cannot be determined
    Choice C
    The two quantities are equal
    Approach to solve this GRE Quantitative Comparison Question

    Step 1: Quantity A: Compute the length of the line segment joining the x and y intercepts of 4x + 3y = 12.
    Step 2: Quantity B: Compute the coordinates of the mid point D.
    Step 3: Quantity B: Compute the length of the median AD.
    Step 4: The Comparison: Compare the length of the line segment joining x and y intercepts of 4x + 3y = 12 and the median AD of the triangle given in Quantity B.

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