Question

Find the coordinates of the point Q on the x–axis which lies on the perpendicular bisector of the line segment joining the points A (–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.

Answer 1

Point Q is the midpoint of AB as the point P lies on the perpendicular bisector of AB.

By mid point formula:

(x₁ + x₂)/2 = (-5+4)/2

= -½

x = -½

Given that, P lies on x axis, so y=0

P(x,y)= (-½ , 0)

Therefore, it is an isosceles triangle