Complete the coordinate proof of the theorem. Given: A B C D is a parallelogram. Prove: The diagonals of A B C D bisect each oth
er. Art: A parallelogram is graphed on a coordinate plane. The horizontal x-axis and vertical y-axis are solid. The vertex labeled as A lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as B lies on begin ordered pair a comma 0 end ordered pair. The vertex labeled as D lies on begin ordered pair c comma b end ordered pair. The vertex C is unlabeled. Diagonals A C and B D are drawn by a dotted lines. Enter your answers in the boxes. The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C( , ), and D(c, b) . The coordinates of the midpoint of AC¯¯¯¯¯ are ( , b2 ). The coordinates of the midpoint of BD¯¯¯¯¯ are ( a+c2 , ). The midpoints of the diagonals have the same coordinates. Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
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Attached you will see the solution using the trig plane and general solutions.
