MathDB

For any two points

A (x_1 , y_1)

and

B (x_2, y_2)

, the distance

r (A, B)

between them is determined by the equality

r(A, B) = | x_1- x_2 | + | y_1 - y_2 |

. Prove that the triangle inequality

r(A, C) + r(C, B) \ge r(A, B)

. holds for the distance introduced in this way .
Let

A

and

B

be two points of the plane (you can take

A(1, 3)

B(3, 7)

). Find the locus of points

C

for which a)

r(A, C) + r(C, B) = r(A, B)

r(A, C) = r(C, B).

Problem Statement