Question

The circumcentre of the triangle with vertices (0,0),(3,0) and (0,4) is ;-

• A. $(1,1)$
• B. $(2,\frac{3}{2})$
• C. $(\frac{3}{2},2)$
• D. None of these

Answer 1

The correct option is C $(\frac{3}{2},2)$

Step 1 :

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

Finding the midpoint of AB

$=(\frac{3+0}{2},\frac{0+0}{2})$

$=(\frac{3}{2},0)$

Now by finding the slope of $AB=(\frac{0-0}{3-0}=0)$

Now , slope of perpendicular bisector is negative reciprocal of AB that is slope of the bisector $=\infty .$

Step 2 :

Finding the equation of AB with the point $(\frac{3}{2},0)$ is

$x=\frac{3}{2}$ 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 $(\frac{3}{2},2)$.