Question

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)

Answer 1

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.