Question

find the coordinates of point Q on the x-axis which lies on perpendicular bisector of the line segment joining the points A( - 5, - 2 )and B(4, - 2 )name the type of the Triangle formed by joining the points Q A B

Answer 1

let the point be Q (a , 0)

point of intersection of perpendicular bisector and line AB 
                                               = ((-5 + 4)/2 , (-2 - 2)/2 
                                               = (-1/2 , -2)

   equation of AB is y= -2
 so equation of  perpendicular bisector is x+ b = 0   b is any constant

as (-1/2 , -2 ) lies on it so -1/2 + b = 0  so b= 1/2

so equation of perpendicular bisector is  x + 1/2 = 0

and triangle formed is isosceles triange