Question

The triangle whose vertices are (0,7,-10), (1,6,-6) and (4,9,-6) is a ___.

• A. acute-angled triangle
• B. Right-angled triangle
• C. scalene triangle
• D. isosceles triangle

Answer 1

Answer: (B), (D)

The correct options are
B

Right-angled triangle

D

isosceles triangle

Let the vertices of the triangle be A(0,7,-10), B(1,6,-6) and C(4,9,-6)

$AB=\sqrt{(1-0{)}^2+(6-7{)}^2+(-6-(-10){)}^2}=\sqrt{1^2+1^2+4^2}=\sqrt{18}BC=\sqrt{(4-1{)}^2+(9-6{)}^2+(-6-(-6){)}^2}=\sqrt{3^2+3^2+0^2}=\sqrt{18}AC=\sqrt{(4-0{)}^2+(9-7{)}^2+(-6-(-10){)}^2}=\sqrt{4^2+2^2+4^2}=\sqrt{36}$

$Here,AB=BC\&A{B}^2+B{C}^2=A{C}^2$
Hence, the triangle is isosceles as well as right-angled.