SOLUTION: How to find the area of rectangle with vertices A ( -5,1) B (-3,-1) C (3,5) D (1,7)

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Question 884983: How to find the area of rectangle with vertices A ( -5,1) B (-3,-1) C (3,5) D (1,7)
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
To find the area of a rectangle you take the length of the rectangle times the height of the rectangle. If you graph those points you will find that ab and dc are your heights and ad and bc are your lengths. So we pick one of the lengths and one of the heights, find the distance between the points, and then multiply.

So lets pick AB to be the height and BC to be the length. We now need to find the distance from a to b and b to c. The distance from a to b will be denoted as |AB| and the distance between B to C will be denoted |BC|. To find the distance between two points we use the distance formula which is d=sqrt%28%28x1-x2%29%5E2%2B%28y2-y1%29%5E2%29. Now we can just plug in the points and find the distance. REMEMBER A(-5,1), B(-3,-1), C(3,5)

|AB| = d=sqrt%28%28x1-x2%29%5E2%2B%28y2-y1%29%5E2%29
=d=sqrt%28%28-5-%28-3%29%29%5E2%2B%281-%28-1%29%29%5E2%29
=d=sqrt%28%28-5%2B3%29%5E2%2B%281%2B1%29%5E2%29
=d=sqrt%28%28-5%2B3%29%5E2%2B%281%2B1%29%5E2%29
=d=sqrt%28%28-2%29%5E2%2B%282%29%5E2%29
=d=sqrt%284%2B4%29
=d=2%2Asqrt%282%29

|BC| = d=sqrt%28%28x1-x2%29%5E2%2B%28y2-y1%29%5E2%29
= d=sqrt%28%28-3-3%29%5E2%2B%28-1-5%29%5E2%29
= d=sqrt%28%28-6%29%5E2%2B%28-6%29%5E2%29
= d=sqrt%2836%2B36%29
= d=sqrt%2872%29
= d=6%2Asqrt%282%29
So the area of the rectangle is |AB|*|BC|
|AB|*|BC| = 2%2Asqrt%282%29+%2A+6%2Asqrt%282%29
= 12(2)
= 24