Use an algebraic proof to show that the points A(-3, 1), B(0, 4), C(0, 2), and D(-3, -1) form a parallelogram, not a rectangle. (No points will be given for drawing a diagram).

The points (3, 0), (-1, 1), (5, 1) and (1, 2) are the vertices of a parallelogram ABC D. If ABCD is translated by v = (3, –2), find the vertices of the new parallelogram A' B'C' D' . (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in the form of an unordered list of points (*, *), ... ,(*, *).) vertices of A' B'C' D':

A quadrilateral has the vertices D (-4, -1), E (0, -4), F (6.0) and G (0.4). Verify for each pair of adjacent sides that the line segment joining their midpoints is parallel to a diagonal of the quadrilateral.

Find the area of the parallelogram whose vertices are: A(0,0,0) B(5,2,6) C(9,-1,6) D(4,-3,0)