Question

Find the perimeter of quadrilateral ABCD with vertices A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).

Answer 1

Given:

The vertices of a quadrilateral ABCD are A(0, 4), B(4, 1), C(1, -3), and D(-3, 0).

To find:

The perimeter of quadrilateral ABCD.

Solution:

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using the distance formula, we get

`AB=√((4-0)^2+(1-4)^2)`

`AB=√((4)^2+(-3)^2)`

`AB=√(16+9)`

`AB=√(25)`

`AB=5`

Similarly,

`BC=√((1-4)^2+(-3-1)^2)`

`BC=5`

`CD=√((-3-1)^2+(0-(-3))^2)`

`CD=5`

And,

`AD=√((-3-0)^2+(0-4)^2)`

`AD=5`

Now, the perimeter of the quadrilateral ABCD is:

`P=AB+BC+CD+AD`

`P=5+5+5+5`

`P=20`

Therefore, the perimeter of the quadrilateral ABCD is 20 units.