Question on: JAMB Mathematics - 2024

The perpendicular bisector of a line XY is the locus of a point B whose distance from Y is always twice its distance from X.

whose distance from X is always twice its distance from Y

whose distance from Y is always twice its distance from X.

which moves on the line XY

which is equidistant from the points X and Y

Ask EduPadi AI for a detailed answer

Correct Option: B

We are given a point \(B\) such that its distance from Y is always twice its distance from X. This means the ratio of the distances from B to X and from B to Y is 1:2.

Let d_X represent the distance from B to X, and d_Y represent the distance from B to Y. According to the given condition, we have:

\( d_Y = 2 \cdot d_X \)

This suggests that point B lies on a locus where the distance to Y is always twice the distance to X. This condition is satisfied by a specific geometric construction, which is the perpendicular bisector of the line segment XY. The perpendicular bisector divides the segment XY into two equal parts and places any point on it equidistant from X and Y, satisfying the given ratio of distances.