# 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 \(x\)-coordinate of a point is found by measuring the distance from the point to the \(y\)-axis parallel to the \( x \)-axis. Similarly, the \(y\)-coordinate of a point is found by measuring the distance from the point to the \(x \)-axis parallel to the \(y\)-axis. The red point in the above figure has the coordinates \((a, b)\).

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