How to Find Equidistant Points on Y-Axis?
Consider two points A (a, b) and B (p, q) lying at a distance from each other on a two dimensional plane.
We have to find a point on the y-axis which is equidistant from these points. It is known that any point that lies on y-axis is of the form (0, y).
Suppose C is (0, y). According to the problem we can conclude that,
AC = BC
AC2 = BC2
Using distance formula we have,
(0 – a)2 + (y – b)2 = (0 – p)2 + (y – q)2
a2 + y2 + b2 – 2yb = p2 + y2 + q2 – 2yq
2y (q – b) = p2 – q2 – a2 – b2
y = (p2 – q2 – a2 – b2)/2(q – b)
The above value is calculated by substituting the given values of a, b, p and q. This gives us the point required (0, y).
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How to find Equidistant Points on Y-Axis?
Distance formula is used to calculate the distance between any two points in a two-dimensional or three-dimensional plane. To find equidistant points on the y-axis we use the distance formula.