Let's dissect the boy's movement into:

Initial Movement:

The boy travels 2√2 meters at an angle of 135 degrees.
So we can write this movement into its horizontal and vertical components:
Horizontal component: 2√2 * cos(135°) = -2 meters (to the left)
Vertical component: 2√2 * sin(135°) = 2 meters (upwards)
Second Movement:

The boy travels 8 meters to the north.
Now, let's depict this movement on a coordinate plane:.
He travels 2 meters in the left/up direction reaching the point at (-2, 2).
From this point, he travels another 8 meters up to point (-2,10)
To determine the magnitude of the displacement, we'll use Pythagorean's theorem. We have it here;

Displacement = √((-2)^2 + 10^2 ) =√(4 +100) = √104 meter
Magnitude of the Displacement for boy is; √104 meters.