A point P moves in a plane such that its distance from a fixed point O is always 7\text{ c… — JAMB UTME

A point $P$ moves in a plane such that its distance from a fixed point $O$ is always $7\text{ cm}$ . What is the diameter, in $\text{cm}$ , of the geometric locus traced out by point $P$ ?

Answer: 14 cm

Answer

The diameter of the locus traced out by point

P

14\text{ cm}

The locus of a point that maintains a constant distance from a fixed point is a circle. The fixed point

O

is the center of the circle, and the constant distance of

7\text{ cm}

is its radius (

r

). Since the diameter (

D

) of a circle is twice its radius (

D = 2r

), the diameter is

2 \times 7 = 14\text{ cm}

Step-by-Step Solution

Identify the shape of the geometric locus defined by the condition

A circle centered at point

O

with radius

r = 7\text{ cm}

By definition, the set of all points at a fixed distance from a single point forms a circle.

Calculate the diameter using the radius

D = 2 \times 7\text{ cm} = 14\text{ cm}

The diameter of a circle is equal to twice its radius.

Key Concept

Locus of a point at a constant distance from a fixed point

Estimated Time:45s

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