Question

Name the figure formed by plotting the following point. Also, find the area of the figure.

C(0, 4), D(−5, −2), E(1, −2), F(6, 4)

Answer 1

Given:

C(0, 4), D(−5, −2), E(1, −2), F(6, 4)

Step 1: Side Lengths

`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

CD = `sqrt((0 + 5)^2 + (4 + 2)^2)`

= `sqrt(25 + 36)`

= `sqrt61`

DE = `sqrt((1 + 5)^2 + (−2 + 2)^2)`

= `sqrt(36 + 0)`

= 6

EF = `sqrt((6 − 1)^2 + (4 + 2)^2)`

= `sqrt(25 + 36)`

= `sqrt61`

FC = `sqrt((6 − 0)^2 + (4 − 4)^2)`

= `sqrt(36 + 0)`

= 6

Step 2: Identify the Figure

CD  = EF = `sqrt61​`, ... [Opposite sides are equal]

DE = FC = 6

Diagonals will intersect but are not necessarily equal.

The figure is a parallelogram.

Step 3: Use Area Formula for Parallelogram

Points in order:

C(0, 4), D(−5, −2), E(1, −2), F(6, 4)

Area = `1/2 |x_1​y_2 + x_2y_3 + x_3y_4 + x_4y_1 − (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1)|` 

`1/2|(0)(−2) + (−5)(−2) + (1)(4) + (6)(4) − [4(−5) + (−2)(1) + (−2)(6) + 4(0)]|`

`1/2|0 + 10 + 4 + 24 − [−20 − 2 − 12 + 0]`

= `1/2 |38 − (−34)|`

= `1/2(72)`

= 36 square units