Question

A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)

Answer 1

Answer: 82 sq. units .

Explanation:

Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.

Then we plot them on graph ( as provided in attachment)

Length = AB
`=√((9+1)^2+(-1-7)^2)` units [By distance formula :
`√((x_2-x_1)^2+(y_2-y_1)^2)`]

`=√((10)^2+(-8)^2)=√(100+64)=√(164)=2√(41)` units

Width = BC =
`√((-1+5)^2+(7-2)^2)` units

`=√(4^2+5^2)\\\\=√(16+25)\\\\=√(41)`

Area = length x width

=
`2√(41)*√(41)=2*41= 82\text{ sq. units}`

Hence, the area of the rectangle is 82 sq. units .