```
B
/
/
/
/
A
```

- The L1 norm is $|x_2 - x_1| + |y_2 - y_1|$. This is the distance on connecting to an origin $O$:

```
δx
O----B
| /
δy /
| /
|/
A
```

- The L2 norm is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, which is the distance of the vector $AB$, or the hypotenuse of the right angled triangle $AOB$:

```
δx
O----B
| /
δy / L2
| /
|/
A
```

- By triangle inequality, $OA + OB \geq AB$, hence $L_1 = \delta_x + \delta_y \geq L_2$