Question

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Answer 1

Point A and B have coordinates (7,−3) and (1,9) respectively. Find 

(i) the slope of AB.

(ii) the equation of the perpendicular bisector of the line segment AB.

(iii) the value of

Given, co-ordinates of points A are (7,−3) and of B are (1,9)

(i) The slope of AB(m)=(1−7)(9+3)=(−6)12=−2

(ii) Let PQ be the perpendicular bisector of AB intersecting it at M

Now, the co-ordinates of M will be the mid - point of AB

Co-ordinates of M will be

=2(7+1),2(−3+9)=28,26

=(4,3)

The slope of line PQ will be =m−1=(−2)−1=21

Thus, the equation of PQ is 

y−3=21(x−4)

2y−6=x−4

x−2y+2=0

(iii) As point (−2,p) lies on the above line

The point will satisfy the line equation

−2−2p+2