This problem involves distances and directions, which can be represented using vectors or a right-angled triangle.

Let the school be at the origin $(0,0)$.

Niba's position.
Mr. Niba lives 400 m due east of the school. We can represent this as a vector pointing 400 m along the positive x-axis. Let Niba's house be point N.
$N = (400, 0)$

Ako's position.
Mr. Ako lives due south of the school. This means he is along the negative y-axis. Let Ako's house be point A.
$A = (0, -y)$ for some distance $y$.

The direct distance between Niba's house and Ako's house is 500 m. This forms the hypotenuse of a right-angled triangle with the school at the right angle.

The vector diagram would show:

• A point for the school at the origin.
• A line segment from the school to Niba's house, 400 m long, pointing right (East).
• A line segment from the school to Ako's house, $y$ m long, pointing down (South).
• A line segment connecting Niba's house and Ako's house, 500 m long, forming the hypotenuse.

The school, Mr. Niba's house, and Mr. Ako's house form a right-angled triangle.

• One leg is the distance from the school to Niba's house: 400 m.
• The other leg is the distance from the school to Ako's house: Let this be $x$ m.
• The hypotenuse is the direct distance between Niba's and Ako's houses: 500 m.

The Pythagorean theorem states that for a right-angled triangle, $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

The distance covered by Ako's child to reach the school is 300 m.

The distance covered by Ako's child to reach the school is $\boxed{\text{300 m}}$.