1. The problem asks to identify the locus of points that are 4 cm away from a fixed point P. 2. The locus of points at a fixed distance from a point is a circle. 3. The distance from the center point P to any point on the locus is called the radius. 4. Since the distance is 4 cm, the radius of the circle is 4 cm. 5. Therefore, the locus is a circle with radius 4 cm centered at point P. Final answer: The locus of points 4 cm away from a point P is a circle with radius 4 cm centred at P.