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How do you find the area of the rectangle with vertices A(-5,1), B(-3,-1), C(3,5), D(1,7)?

Answer 1

Area #squareABCD=24# sq. units

The area of #square ABCD# could be calculated in several ways.
One would be to divide the rectangle into two triangles, then use the Pythagorean Theorem to find the distances between the points, and finally use Heron's formula to find the areas of the two triangles.

However, I think the method below is easier.

Enclose the rectangle #ABCD# in another rectangle #square PQRS# with sides parallel to the x and y axis:

#Area_(squareABCD)#
#= Area_(squarePQRS)-(Area_(triangleDPA)+Area_(triangleAQB)+Area_(triangle_BRC)+Area_(triangleCSD))#

#Area_(squarePQRS)=8xx8=64#
#Area_(triangleDPA)=Area_(triangleBRC)=(6xx6)/2=18#
#Area_(triangleAQB)=Area_(triangleCSD)=(2xx2)/2=2#

Therefore
#Area_(squarePQRS)=64-(18+2+18+2)=24#

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Answer 2

Julia Adams

To find the area of the rectangle, calculate the distance between opposite vertices to find the length and width of the rectangle. Then, multiply the length by the width.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.