Oblique Coordinates

Geometry Level 2

Did you know that we can have coordinate systems where the coordinate axes are not perpendicular to each other? Such coordinate systems are known as oblique coordinate systems.

The above figure shows an oblique coordinate system. In such systems, the xx-coordinate of a point is found by measuring the distance from the point to the yy-axis parallel to the x x -axis. Similarly, the yy-coordinate of a point is found by measuring the distance from the point to the xx -axis parallel to the yy-axis. The red point in the above figure has the coordinates (a,b)(a, b).

Question: We are given two points: A (1,6)A \ (1,6) and B (5,2)B \ (5,2) in an oblique coordinate system where the angle between the positive axes is 60 60^{\circ} . What is the distance between the two points, ABAB?

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