Question

circumcenter of triangle whose vertices are (1,3),(0,-2),(-3,1)

Answer 1

Answer:

The circumcenter is (-1/3, 2/3)

Step-by-step explanation:

Let A(1,3),B(0,-2),C(-3,1). Slope of AB=(-2–3)/(0–1) =-5/-1=5.

Mid point of AB ( (1+0)/2,(3–2)/2 ) = (1/2,1/2).

Equation of perpendicular bisector of AB is … y - 1/2 = (-1/5)(x - 1/2) => x + 5y -3=0 ……(1)

Slope of BC=( 1+2)/(-3–0) =3/-3= -1

Mid point of BC ( (0–3)/2, (-2+1)/2 ) = (-3/2,-1/2)

Equation of perpendicular bisector of B is……. y - (-1/2) =1{x-(-3/2)} =>y + 1/2 = 1(x + 3/2)

i.e x-y+1 = 0…..(2)

Solving (1) and (2) we get x=-1/3 and y = 2/3.

So the circumcenter is (-1/3, 2/3)

Answer 2

Answer:

x = 1/3, y = 2/3.

Step-by-step explanation:

x = 1/3, y = 2/3.