Question

Which point lies on the perpendicular bisector of a line segment joining the points A bracket ( - 3, 4) and b (3 - 4 )

Answer 1

Given , the points A(-3,4) and B(3,-4)

The perpendicular bisector will bisect the line .

So Let the mid - point of AB be C(x,y)

According to section formula

$x = \frac{ - 3 + 3}{2} \\ \\ = > x = \frac{0}{2} \\ \\ = > x = 0 \\ \\ and \\ y = \frac{ 4 - 4}{2} \\ \\ = > y = \frac{0}{4} \\ \\ = > y = 0$

So required point is C(0,0)

Answer 2

The point that lies on the perpendicular bisector of the line joining the points (-3,4) and (3,-4) is origin (0,0).

• The points joining the line is (-3,4) and (3,-4).
• As the point lies on the perpendicular bisector of the line , it is the midpoint of the lines joining the points (-3,4) and (3,4).
• By midpoint formula,

(x,y) = ( $\farc{x_1+x_2}{2}$ , $\farc{y_1+y_2}{2}$ )

• Therefore,

x = $\farc{x_1+x_2}{2}$

x = $\farc{-3 + 3}{2}$

x = 0

• Similarly,

y = $\farc{y_1+y_2}{2}$

y =$\farc{4+(-4)}{2}$

y = 0

• The point that lies on the perpendicular bisector of the line segment joining the point (-3,4) and (3,-4) is (0,0) that is origin.