Which of the following figures is formed by the points whose coordinates are (0,7,10), (-1,6,6), (-4,9,6)?a)a right-angled triangleb)an equaliaterna trianglec)an isosceles and right - angled triangled)an isosceles triangleCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

The distance between two points in a three dimensional can be calculated as :-

d = [(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]^½

The coordinates are P(0,7,10), Q(-1,6,6), R(-4,9,6)

PQ = [(0+1)²+ (7-6)² + (10-6)^2]^½

PQ = [1+1+16]^½

PQ = [18]^½

QR = [(-1-4)² + (6-9)²+ (6-6)^2]^½

QR = [9+9+0]

QR = [18]^½

PR = [(0+4)² + (7-9)² + (10-6)^2]^½

PR = [16 + 4 + 16]^½

PR = 6

As we can see that (PR)² = (QR)² + (PQ)²

I.e. isoceles and right triangle

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