What is the area of a rectangle with vertices at #(-4, 0), (-3, 1), (0, -2),# and #(-1, -3)#?

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Answer 1 · 2017-07-27T12:50:30

The area of the rectangle is #=6u^2#

Let the vertices be

#A=(-4,0)#

#B=(-3,1)#

#C=(0,-2)#

#D=(-1,-3)#

The area of the rectangle #ABCD# is twice the area of the triangle

#DeltaABC#

The area of the triangle #DeltaABC# is given by the determinant

#area=1/2|(x_1,y_1,1),(x_2, y_2,1),(x_3,y_3,1)|#

#=1/2|(-4,0,1),(-3,1,1),(0,-2,1)|#

#=1/2(-4*(1*1+1*2)-0+1*(6-0))#

#=1/2|-6|=3u^2#

Area of the rectangle is #=6u^2#