Question

The equation of sides of triangle are x+y-5=0,x-y+1=0 and y-1=0 then the circum center is

Answer 1

Answer:

(2,1) is the circumcentre

Step-by-step explanation:

Finding the vertices of the triangle by solving the given equations.

x + y = 5                                    x + y = 5                                     x - y = -1

x - y  = -1                                      y = 1                                            y = 1

2x = 4                                           x = 4                                           x = 0

x = 2                                              (4,1)                                             (0,1)

y = 3

(2,3)

The vertices of the triangle are - (2,3) (4,1) (0,1)

These 3 points are coordinates of a right angled triangle (TO PROOVE -

DISTANCE FORMULAE AND PYTHAGORUS THEOREM). The triangle is right angled at the point (2,3).

For a right angled triangle, the circumcenter is the midpoint of the hypotnuese.

The midpoint of the hypotnuese = (2,1)