Question

For the triangle formed by the point $(4,8),(2,8),(4,12)$

• A. Orthocentre $\equiv (5,7)$
• B. Orthocentre $\equiv (4,8)$
• C. Circumcentre $\equiv (3,10)$
• D. Centroid $\equiv (\frac{10}{3},\frac{28}{3})$

Answer 1

Answer: (B), (C), (D)

Centroid $\equiv (\frac{10}{3},\frac{28}{3})$

Since $A{B}^2=A{C}^2=B{C}^2$
$\angle A={90}^o$
Orthocentre $\equiv (4,8)$


Circumcentre $\equiv$ middle point of hypotenuse $=(3,10)$
Centroid $=(\frac{10}{3},\frac{28}{3})$