Question

The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are

Options

• (0, 2)

•  (3, 0)

•  (0, 3)

•  (2, 0)

Answer 1

TO FIND: The coordinates of a point on x axis which lies on perpendicular bisector of line segment joining points (7, 6) and (−3, 4).

Let P(x, y) be any point on the perpendicular bisector of AB. Then,

PA=PB

                  `sqrt((x -7)^2 + (y -6)^2) = sqrt((x-(-3))^2+(y-4)^2)`

                    `(x-7)^2+ (y - 6)^2 = (x +3)62 + (y-4)^2`

`x^2 - 14x + 49 +y^2 - 12y +36 = x^2 +6x +9 +y^2 -8y + 16`

-14x - 6x - 12y - 8y + 49 +36 -9 - 16 = 0

                               - 20x + 20y + 60 = 0

                                             x - y - 3 = 0

x - y = 3

 

On x-axis y is 0, so substituting y=0 we get x= 3

Hence the coordinates of point is (3,0) .