GRE-Style: Coordinate Geometry

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Coordinate Geometry Finding the exact distance between two plotted points Points A(1, 2) and B(5, 5) are plotted on a coordinate plane. What is the distance between them? Nice work — you turned two plotted points into an exact distance, the same move behind most GRE coordinate-geometry questions. The distance formula IS the Pythagorean theorem: treats the horizontal gap and vertical gap as the two legs of a right triangle, and the distance as its hypotenuse. Subtract coordinates in the same order both times: using x_2 - x_1 and y_2 - y_1 (or consistently reversed) keeps the signs sensible — squaring erases the sign anyway, so either consistent order works. Simplify the radical whenever it's a perfect square: collapses to the whole number 5 — always check before leaving an answer as a messy radical. Result: A(1,2) to B(5,5) is exactly 5 units — the legs 4 and 3 form the well-known right triangle. Whenever a GRE problem gives you two coordinate points, the distance formula turns the picture into a single number — no need to measure anything by eye.

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