Q. 93.8( 4 Votes )

# Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of an isosceles right-angled triangle.

Answer :

**Given:** Points are A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6)

**To prove:** the triangle formed by given points is an isosceles right-angled triangle

Isosceles right-angled triangle is a triangle whose two sides are equal and also satisfies Pythagoras Theorem

**Formula used:**

The distance between any two points (a, b, c) and (m, n, o) is given by,

Therefore,

Distance between A(0, 7, 10) and B(-1, 6, 6) is AB,

Distance between B(-1, 6, 6) and C(-4, 9, 6) is BC,

Distance between A(0, 7, 10) and C(-4, 9, 6) is AC,

= 6

Since, AB = BC

AB^{2} + BC^{2}

= 18 + 18

= 36

= AC^{2}

As, AB = BC and AB^{2} + BC^{2} = AC^{2}

Thus, **Δ ABC is an isosceles-right angled triangle**

**Hence** **Proved**

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