Question

What is the area of a rectangle with vertices at ​ (−6, 3)(−6, 3) ​, ​ (−3, 6)(−3, 6) ​ , (1, 2)(1, 2) , and (−2, −1)(−2, −1) ? Do not round any side lengths.

Answer 1

well, find the legnth and width because lenth times width =area
we just need to find 2 differnd distances

the distance between 2 points, (x1,y1) and (x2,y2) is

`D= √((x2-x1)^2+(y2-y1)^2)`
let's find distance between (-6,3) and (-3,6)

`D= √((-3-(-6))^2+(6-3)^2)`=√18=3√2

the other one
from (-3,6) to (1,2)

`D= √((1-(-3))^2+(2-6)^2)`=√32=4√2

area=legnth times width
legnth=4√2
width=3√2
area=4√3 times 3√2=12*2=24

the area is 24