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Question
Verify that the following points taken in order to form the vertices of a rhombus
A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)
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Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((7 - 3)^2 + (6 + 2)^2`
= `sqrt((4)^2 + (8)^2`
= `sqrt(16 + 64)`
= `sqrt(80)`
BC = `sqrt((-1 - 7)^2 + (2 - 6)^2`
= `sqrt((- 8)^2 + (- 4)^2`
= `sqrt(64 + 16)`
= `sqrt(80)`
CD = `sqrt((-5 + 1)^2 + (-6 - 2)^2`
= `sqrt((- 4)^2 + ( - 8)^2`
= `sqrt(16 + 64)`
= `sqrt(80)`
AD = `sqrt((-5 - 3)^2 + (- 6 + 2)^2`
= `sqrt((- 8)^2 + (- 4)^2`
= `sqrt(64 + 16)`
= `sqrt(80)`
AB = BC = CD = AD = `sqrt(80)`
All the four sides are equal.
∴ ABCD is a rhombus.
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