Find the area of the parallelogram with vertices a(−3. 0). b(−1. 3). c(5. 2). and d(3. −1).


6. o 01 points i Previous Answers scalos 124.027 Find the area of the parallelogram with vertices A(-3, o), B(-1, 3), c(5, 2), and D(3, -1). Need Help? Read It Talk to a Tutor 12 points Previous Answers scalc8 12 4 029 Consider the points below.

Answer

The area of the parallelogram with the vertices A:(-3,0), B;(-1,3),C:(5,2),D:(3,-1) is ||DC|x|AD||. Now DC = (3,-1)-(5,2) = (-2,-3) and AD = (3,-1)-(-3,0) = (6,-1). Therefore, DC x AD = | i   j   k |                                                                                                                                          |-2 -3 0 |                                                                                                                                             | 6 -1 0 | = i( -3*0-0*-1)-j(-2*0-0*6)+k(-2*-1-6*-3) = k(2+18) = 0i +0 j+20k.

Hence the area of the parallelogram ABCD is |0i +0 j+20k | = √(02 +02 +202) = √400 = 20.   

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