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 .

Step-by-step 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 $=\sqrt{(9+1)^2+(-1-7)^2}$ units  [By distance formula : $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$]

$=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}$ units

Width = BC = $\sqrt{(-1+5)^2+(7-2)^2}$ units

$=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}$

Area = length x width

= $2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}$

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