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  • Write the coordinates of a point P on x axis which is equidistant from the points A(– 2, 0) and B(6, 0).    

Write the coordinates of a point P on x axis which is equidistant from the points A(– 2, 0) and B(6, 0).

 

 

Answers (1)

Given points are A(-2,0) and B(6,0). Both points lie on x-axis because y-coordinates of both points A & B is 0.

Point P on the x-axis which is equidistant from points A & B.

It is clear that point A, point B and point P lie on the x-axis, and P is the midpoint of A & B.

\begin{align*} \text{Midpoint (P)} & = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right )\\ P & =\left(\frac{-2 + 6}{2}, \frac{0 + 0 }{2} \right ) \\ P & = \left(\frac{4}{2}, \frac{0}{2} \right ) \\ P & = (2,0) \end{align*}

Therefore the coordinates of points P are (2,0)

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