Unattributed TMUA Mock Set A Paper 2 · Question 14

In a Cartesian coordinate system, define the “Manhattan distance” between two points as the sum of the absolute differences of their coordinates, so that

d(P,Q)=|x_1-x_2|+|y_1-y_2|

is the Manhattan distance between the two points $P$ and $Q$ . Consider the following statements:

I. The set of points with a Manhattan distance of 1 from the origin forms a circle.
II. The set of points with a Manhattan distance of 1 from the origin forms a square.
III. The set of points whose absolute difference of Manhattan distances from $M(-1,0)$ and $N(1,0)$ is 1 forms two parallel lines.
IV. The set of points whose sum of Manhattan distances from $M(-1,0)$ and $N(1,0)$ is 6 forms a hexagon with an area of 16.

How many statements must be true?

ANone of them

1

2

3

4

examday

Unattributed TMUA Mock Set A Paper 2 · Q14