Question

The perimeter of the triangle formed by the
points (1,0,0),(0,1,0),(0,0,1) is​

Answer 1

Answer :

The perimeter of the triangle = 3√2 units

Step-by-step explanation :

The distance between points A (x₁,y₁,z₁) and B (x₂,y₂,z₂) is given by,

 $\bf AB = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Let

• P (1,0,0)

• Q (0,1,0)

• R (0,0,1)

Let's first find the length of the sides.

P (1,0,0) and Q (0,1,0) :

PQ = √(0-1)² + (1-0)² + (0-0)²

PQ = √(-1)² + 1² + 0

PQ = √1 + 1

PQ = √2 units

Q (0,1,0) and R (0,0,1) :

QR = √(0-0)² + (0-1)² + (1-0)²

QR = √0 + (-1)² + 1²

QR = √1 + 1

QR = √2 units

P (1,0,0) and R (0,0,1) :

PR = √(0-1)² + (0-0)² + (1-0)²

PR = √(-1)² + 0 + 1²

PR = √1 + 1

PR = √2 units

PQ = QR = PR = √2 units

Since the length of all sides are equal, it's an equilateral triangle.

The perimeter of the triangle is the sum of the lengths of all sides.

➙ The perimeter of the triangle = PQ + QR + PQ

➙ The perimeter of the triangle = √2 + √2 + √2

➙ The perimeter of the triangle = 3√2 units