Question

The points A(-3, 3), B(0, 7), C(4, 10), D(1, 6) create parallelogram ABCD. What is the perimeter of parallelogram ABCD, in units?

Answer 1

Given:

The points A(-3, 3), B(0, 7), C(4, 10), D(1, 6) create parallelogram ABCD.

To find:

The perimeter of parallelogram ABCD.

Solution:

Distance formula is

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula, find the side length of parallelogram.

`AB=√((0-(-3))^2+(7-3)^2)`

`AB=√((3)^2+(4)^2)`

`AB=√(9+16)`

`AB=√(25)`

`AB=5`

Similarly,

`BC=√(\left(4-0\right)^2+\left(10-7\right)^2)=5`

`CD=√(\left(1-4\right)^2+\left(6-10\right)^2)=5`

`AD=√(\left(1-\left(-3\right)\right)^2+\left(6-3\right)^2)=5`

Now,

Perimeter of ABCD is

`P=AB+BC+CD+AD`

`P=5+5+5+5`

`P=20`

Therefore, the perimeter of parallelogram ABCD is 20 units.