Question

The x-coordinate of the point lying on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is_______.

Answer 1

Perpendicular bisectors divides the line segment in two equal parts.

$\mathrm{Mid}\mathrm{point}\mathrm{of}\left(x_1,y_1\right)\mathrm{and}\left(x_2,y_2\right)\mathrm{is}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right).$


Therefore, the mid point of A(–2, –5) and B(2, 5)
$$\begin{gathered} =\left(\frac{-2+2}{2},\frac{-5+5}{2}\right) \\ =\left(\frac{0}{2},\frac{0}{2}\right) \\ =\left(0,0\right) \end{gathered}$$

Hence, the x-coordinate of the point lying on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is 0.