Verify the following:
(0, 7, –10), (1, 6, – 6) and (4, 9, – 6) are the vertices of an isosceles triangle.

Question

Verify the following: (0, 7, –10), (1, 6, – 6) and (4, 9, – 6) are the vertices of an isosceles triangle.

Philoid · Accepted Answer

Let points be

P(0, 7, –10), Q(1, 6, – 6) & R(4, 9, – 6)

If any 2 sides are equal, it will be an isosceles triangle

Calculating PQ

P ≡ (0, 7, – 10) and Q ≡ (1, 6, – 6)

Distance PQ

Here,

x₁ = 0, y₁ = 7, z₁ = – 10

x₂ = 1, y₂ = 6, z₂ = – 6

Distance PQ

Calculating QR

Q ≡ (1, 6, – 6) and R ≡ (4, 9, – 6)

Distance QR

Here,

x₁ = 1, y₁ = 6, z₁ = – 6

x₂ = 4, y₂ = 9, z₂ = – 6

Distance QR

Since PQ = QR

∴ 2 sides are equal

Hence PQR is an isosceles triangle.

Verify the following:(0, 7, –10), (1, 6, – 6) and (4, 9, – 6) are the vertices of an isosceles triangle.