What is the area of a parallelogram with corners at these coordinates on a plane: (-2,-1), (-12,-4), (9,-4), (-1,-7)?

1 Answer

Let see the figure which shows the parallelogram with given vertices

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As the diagonal of a parallelogram BC divides into two congruent triangles, which implies the triangles have same area.

So, the area of the parallelogram will be 2 times the area of the triangle ABC.

We know from analytical geometry that the area of a triangle with given vertices is

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where #(x_A,y_A)# ,#(x_B,y_B)#,#(x_C,y_C)# are the coordinates of points A,B,C.

Now we just have to replace the values in the formula above and find the value for #E_(ABC)#

Hence the area of the parallelogram is

#E_(ABCD)=2*E_(ABC)#