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प्रश्न
Name the figure formed by plotting the following point. Also, find the area of the figure.
A(6, 6), B(2, 2), C(6, −2), O(10, 2)
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उत्तर
Given:
A(6, 6), B(2, 2), C(6, −2), O(10, 2)
Find the lengths using the distance formula:
`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`
AB = `sqrt((6 − 2)^2 + (6 − 2)^2)`
= `sqrt(16 + 16)`
= `sqrt32`
BO = `sqrt((10 − 2)^2 + (2 − 2)^2)`
= `sqrt(64 + 0)`
= 8
OC = `sqrt((10 − 6)^2 + 2 − (−2)^2)`
= `sqrt(16 + 16)`
= `sqrt32`
CA = `sqrt((6 − 6)^2 + (−2 − 6)^2)`
= `sqrt(0 + 64)`
= 8
AB = OC = `sqrt32`
BO = CA = 8
Plot the points or rearrange them in the order:
A(6, 6), B(2, 2), C(6, −2), O(10, 2)
AB = BO = OC = CA =`sqrt32` ...[All sides are equal]
Diagonal AC = 8 ...[Both diagonals are equal and perpendicular.]
Diagonal BO = 8
Therefore, the figure is a square & the area is 32 square units.
