Question

Coordinate of the vertices of $\Delta ABC$ are $(12,8)$, $(-2,6)$ and $(6,0)$ then the correct statement(s) are?

• A. Triangle is right but not isosceles
• B. Triangle is right as well as isosceles
• C. Triangle is obtuse
• D. The product of abscissae of the centroid, orthocentre and circumcentre is $160$

Answer 1

The correct option is B Triangle is right as well as isosceles

Given $A(12,8)B(-2,6)C(6,0)$

$\overrightarrow{AB}=\sqrt{(12+2{)}^2+(8-6{)}^2}$

$=\sqrt{{14}^2+2^2}$

$=\sqrt{200}$

$\overrightarrow{BC}=\sqrt{(-2-6{)}^2+(6-0{)}^2}$

$=\sqrt{8^2+6^2}$

$=\sqrt{100}=10$

$\overrightarrow{CA}=\sqrt{(12-6{)}^2+(6-0{)}^2}$

$=\sqrt{6^2+6^2}$

$=10$

$A{B}^2=200,B{C}^2=100,C{A}^2=100$

as $B{C}^2+C{A}^2=A{B}^2$

$\therefore$ it is right $\angle ed$ triangles