Question

Name the quadrilateral formed by plotting the following point. Also, find the perimeter.

A(0, 4), B(4, 7), C(8, 4), D(4, 1)

Answer 1

Given:

A(0, 4), B(4, 7), C(8, 4), D(4, 1)

Step 1: Find Side Lengths Using Distance Formula

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

AB = `sqrt((4 − 0)^2 + (7 − 4)^2)`

= `sqrt(16 + 9)`

= `sqrt25`

= 5

BC = `sqrt((8 − 4)^2 + (4 − 7)^2)`

= `sqrt(16 + 9)`

= `sqrt25`

= 5

CD = `sqrt((4 − 8)^2 + (1 − 4)^2)`

= `sqrt(16 + 9)`

= `25`

= 5

DA = `sqrt((0 − 4)^2 + (4 − 1)^2)`

= `sqrt(16 + 9)`

= `sqrt25`

= 5

Step 2: Identify the Quadrilateral

All four sides are equal. 

Figure = Rhombus

Step 3: Find the Perimeter

Perimeter = AB + BC + CD + DA

= 5 + 5 + 5 + 5

= 20 units