Question

The line $3x+4y-24=0$ intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is:

• A. $(2,3)$
• B. $(3,3)$
• C. $(4,3)$
• D. None of the above

Answer 1

The correct option is C $(4,3)$

Given that:

$3x+4y-24=0$

Its $x$-intercept $=(8,0)$

and its $y$-intercept $=(0,6)$

Since, $AOB$ is a right angled triangle.

So, mid-point of the hypotenuse is the circumcentre.

Hence, circumcentre$=(4,3)$ $[\therefore \frac{8+0}{2},\frac{0+6}{2}=(4,3\left)\right]$

Hence, C is the correct option.