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The points A = [3, 2], B = (-1,4], C=[-2,-2) and D= [3,-1] form a quadrangle ABCD in the xy-plane. The line segments AC and BD intersect each other in a point E. Determine the coordinates of E. Give your answer in the form [a, b] for the correct values of a and b

Let A, B, C and D be as in the previous exercise. That is A=(3, 2), B=(-1,4), C-1-2,-2 and D= [3, -1]. Let O= [0,0] denote the origin. Which of the following triangles has the largest area? O O ΔΑΒΟ ABCO O ACDO O ADAO

We want to change the coordinate of the point O such that the triangle ADAO has the largest area amongst the triangles AABO, ABCO, ACDO, ADAO, and that it is the only one with this area. Give an example of such new coordinates. Give your answer in the form [a, b] for the correct values of a and b Of note: there is not one, unique, correct answer. There are multiple choices for a and b possible. You just need to provide one example.