Question

If the points (0, 1, 2), (2, –1, 3) and (1, –3, 1) are the vertices of a triangle then the triangle is

Answer 1

Given info : the points (0, 1, 2) , (2, -1, 3) and (1, -3, 1) are the vertices of a triangle.

Then identify which type of triangle formed by three points.

Solution : let A(0, 1, 2) , B(2, -1, 3) and C(1, -3, 1)

AB = √{(2 - 0)² + (-1 - 1)² + (3 - 2)²}

= √(4 + 4 + 1) = 3

BC = √{(2 - 1)² + (-1 + 3)² + (3 - 1)²}

= √(1 + 4 + 4) = 3

CA = √{(1 - 0)² + (-3 - 1)² + (1 - 2)²}

= √(1 + 16 + 1) = 3√2

Here we see AB = BC so triangle is isosceles.

And also CA² = AB² + BC² , so triangle is right angled.

Therefore triangle formed by points is right angled isosceles triangle.

Answer 2

Step-by-step explanation:

isosceles right triangle