Question

For points P = (x₁, y₁) and Q = (x₂, y₂) of the coordinate plane, a new distance d(P, Q) is defined by d(P, Q) = |x₁ - x₂| + |y₁ - y₂|.

Let O = (0, 0) and A = (3, 2). Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.

Answer 1

d : (P, Q) = |x₁ - x₂| + |y₁ - y₂|.

It is new method of representing distance between two points P and Q and in future very important in coordinate gerometry.

Now, let P(x, y) be any point in the first quadrant. We have

The graph is given in adjoining figure.

Comments

Great explanation
Thx