Question

Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).

Answer 1

d is the answer

Explanation:

Answer 2

The area of rectangle is
`72\ units^(2)`

Explanation:

see the attached figure with letters to better understand the problem

Let

`A(3.10),B(12,1),C(16,5),D(7,14)`

we know that

The area of rectangle is equal to

`A=(AB)(BC)`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance AB

we have

`A(3.10),B(12,1)`

substitute in the formula

`AB=\sqrt{(1-10)^(2)+(12-3)^(2)}`

`AB=\sqrt{(-9)^(2)+(9)^(2)}`

`AB=√(162)\ units`

Find the distance BC

we have

`B(12,1),C(16,5`

substitute in the formula

`BC=\sqrt{(5-1)^(2)+(16-12)^(2)}`

`BC=\sqrt{(4)^(2)+(4)^(2)}`

`BC=√(32)\ units`

Find the area of rectangle

`A=(√(162))*(√(32))=72\ units^(2)`