Question

The circumcentre of a triangle with the vertices (a,0). (0,b) and (a, b).​

Answer 1

Step-by-step explanation:

Step 1 :

Given coordinates A(0,0),B(3,0),C(0,4)

Finding the midpoint of AB

=(

2

3+0

,

2

0+0

)

=(

2

3

,0)

Now by finding the slope of AB=(

3−0

0−0

=0)

Now , slope of perpendicular bisector is negative reciprocal of AB that is slope of the bisector =∞.

Step 2 :

Finding the equation of AB with the point (

2

3

,0) is

x=

2

3

is equation of the bisector of AB.

Similarly, if we find the equation of bisector of AC we have

Equation of bisector of AC=>y=2

Step 3 :

Hence the coordinates of the circumcenter of the given triangle is (

2

3

,2).