Slope of side BC = \((\frac{6-3}{1-2} = (\frac{3}{-1}) = -3\)
Slope of perpendicular bisector of BC is 1/3 and the line passes through \((\frac{3}{2}, \frac {9}{2})\)
Equation of the perpendicular bisector of side BC is \((y-\frac{9}{2})= \frac {1}{3} (x-\frac{3}{2})\)
3(2y – 9) = (2x – 3)
6y – 27 = 2x – 3
2x – 6y + 24 = 0
∴ x – 3y + 12 = 0 Since both the points A and C have same x co-ordinates i.e. 1
the points A and C lie on the line x = 1.
AC is parallel to Y-axis and therefore, perpendicular bisector of side AC is parallel to X-axis.
Since, the perpendicular bisector of side AC passes through E(1, 5).
The equation of perpendicular bisector of side AC is y = 5.
Slope of side AB = \((\frac{3-4}{2-1})\)= -1
Slope of perpendicular bisector of AB is 1 and the line passes through \((\frac{3}{2}, \frac {7}{2})\)
Equation of the perpendicular bisector of side AB is \((y-\frac{7}{2})= 1 (x- \frac {3}{2})\)
2y – 7 = 2x – 3
2x – 2y + 4 = 0
∴ x – y + 2 = 0
