A(7-1), B(6, 4) and C(5, 5) are three points in a plane.
1). Find the equations of the
perpendicular bisectors of AB and AC
(ü) Determine the point of
intersection of the perpendicular
bisectors in (i).
(WAEC)

The answer is below

Step-by-step explanation:

The equation of the line passing through two points is given by:

The equation of line AB is:

The midpoint of two lines is given as:

The equation of line AC is:

The midpoint of two lines is given as:

The product of the slope of a perpendicular bisector of a line and the slope of the line is -1. That is m1m2 = -1

The slope of the perpendicular bisector of AB is:

m(-5)=-1

m=1/5

The equation of the perpendicular bisector of AB passing through (6.5,1.5) is:

The slope of the perpendicular bisector of AB is:

m(-3)=-1

m=1/3

The equation of the perpendicular bisector of AB passing through (6,2) is:

2) The point of intersection is gotten by solving y = 1/5 x -8.25 and y = 1/3 x-4.33 simultaneously.

Subtracting the two equations from each other gives:

0= -0.133x - 3.92

-0.133x = 3.92

x = -29.5

Put x = -29.5 in y = 1/5 x -8.25 i.e:

y = 1/5 (29.5) -8.25

y = -14.16

The point of intersection is (-29.5, -14.16)

36

step-by-step explanation: