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प्रश्न
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.
उत्तर
Let the vertices of triangle ABC be A(0, 7, –10), B(1, 6, –6) and C(4, 9, –6).
Now, AB = `sqrt((1 - 0)^2 + (6 - 7)^2 + (-6 +10)^2)`
= `sqrt((1)^2 + (-1)^2 + (4)^2)`
= `sqrt(1 + 1 + 16)`
= `sqrt18`
= `3sqrt2`
BC = `sqrt((4 - 1)^2 + (9 - 6)^2 + (-6 + 6)^2)`
= `sqrt((3)^2 + (3)^2`
= `sqrt(9 +9)`
= `sqrt18`
= `3sqrt2`
CA = `sqrt((0 - 4)^2 + (7 - 9)^2 + (-10 + 6)^2)`
= `sqrt((-4)^2 + (-2)^2 + (-4)^2)`
= `sqrt(16 + 4 + 16)`
= `sqrt36`
= 6
Here, AB = BC ≠ CA
Hence, the given vertices AB = BC are of the isosceles triangle.
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