Question

The circumcenter of a triangle formed by the lines X+y-1=0,x-y-1=0 is

Answer 1

Answer:

The circumcenter of the triangle is: (0,0)

Step-by-step explanation:

Let ΔABC be formed by the lines $x+y-1=0$ and $x-y-1=0$.

the vertices of triangle is given as:

A(0,1),B(1,0),C(0,-1).

Now length AB=$\sqrt{2}$ units

Length BC=$\sqrt{2}$ units

and Length AC=2 units

As looking at the length of sides of ΔABC we could see that this triangle is an right angled triangle as:

$AC^{2}=AB^{2}+BC^{2}$

So, the circumcenter will lie at the mid-point of side AC.

Mid-point of AC= $(\dfrac{0+0}{2},\dfrac{1+(-1)}{2})=(0,0)$

(Since the mid-point of two points (a,b) and (c,d) is given by:

$(\dfrac{a+c}{2},\dfrac{b+d}{2})$ )

Hence, the circumcenter of the triangle formed by the given two line is (0,0).