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प्रश्न
Points A (-3, -2), B (-6, a), C (-3, -4) and D (0, -1) are the vertices of quadrilateral ABCD; find a if 'a' is negative and AB = CD.
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उत्तर
AB = CD
AB2 = CD2
(- 6 + 3)2 + (a + 2)2 = (0 + 3)2 + (- 1 + 4)2
9 + a2 + 4 + 4a = 9 + 9
a2 + 4a - 5 = 0
a2 - a + 5a - 5 = 0
a(a - 1) + 5 (a - 1) = 0
(a - 1) (a + 5) = 0
a = 1 or - 5
It is given that a is negative, thus the value of a is - 5.
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By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
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= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
