Question

Find the circumcentre of the triangle whose vertices are (1,0),(-1,2),(3,2) ​

Answer 1

Step-by-step explanation:

Let the coordinates of the vertices of the triangle are A(1,1),B(2,−1) and C(3,2)

Now, Lets find the distance between each of the three points.

We will use the distance formula to find the distance between AB,BC and AC

Thus AB= (2−1) 2+(−1−1) 2= 5

BC= (3−2) 2 +(2+1) 2 = 10

AC= (3−1) 2+(2−1) 2= 5

NowAB

2+AC 2 =10=BC 2

Thus it form a right angled triangle, right angled at A.

Now the circumcentre will be the mid-point of the hypotenuse BC.

Thus mid-point of BC is ( 22+3 , 2−1+2 )=( 25, 21 ).

And the circumradius is the half the length of BC

⇒ Circumradius =

2

10