In Problems 2528 the given three points form a triangle Dete

In Problems 25-28, the given three points form a triangle. Determine which triangle are isosceles and which are right triangles. (0, 0, 0), (3, 6, - 6), (2, 1, 2) (0, 0, 0), (1, 2, 4), (3, 2, 2 Squareroot 2) (1, 2, 3), (4, 6, 4) (1, 1, - 1), (1, 1, 1), (0, -1, 1)

Solution

25. Let A(0,0,0), B(3,6,-6),C(2,1,2)

AB=sqrt((3-0)²+(6-0)²+(-6-0)²)= 9

BC=sqrt( (2-3)²+(1-6)²+(2-(-6))²)=sqrt90

AC=sqrt((2-0)²⁾+(1-0)²+(2-0)²)=3

Here we are getting

AB²+AC²=BC²

Hence it is a right triangle

Similarly we have to check each questions and if two sides are equal then the triangle is isosceles and if they follows pythagorean theorem then its right triangle