Question

The triangle formed by three points A(1, -2, -3), B(2, -3, -1), C(3, -1, -2) is:

(a) Isosceles right angled triangle
(b) Equilateral triangle
(c) Scalene triangle
(d) Acute triangle​

Answer 1

Answer: It is equilateral triangle

Answer 2

The required "option (b) Equilateral triangle" is correct.

Step-by-step explanation:

Given, the three points of triangle =  A(1, -2, -3), B(2, -3, -1) and  C(3, -1, -2)

To find, the triangle = ?

We know that,

Using distance formula,

$\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2}$

AB = $\sqrt{(2-1)^2+(-3+2)^2+(-1+3)^2}$

= $\sqrt{(1)^2+(-1)^2+(2)^2}$

= $\sqrt{1+1+4}$

= $\sqrt{6}$

BC = $\sqrt{(3-2)^2+(-1+3)^2+(-2+1)^2}$

= $\sqrt{(1)^2+(2)^2+(-1)^2}$

= $\sqrt{1+4+1}$

= $\sqrt{6}$

Also, CA = $\sqrt{(3-1)^2+(-1+2)^2+(-2+3)^2}$

= $\sqrt{(2)^2+(1)^2+(1)^2}$

= $\sqrt{4+1+1}$

= $\sqrt{6}$

∴ AB = BC = CA = $\sqrt{6}$ all three sides are equal.

The given three points are equilateral triangle.

Thus, the required "option (b) Equilateral triangle" is correct.