Question

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 other.

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.

Answer 1

The other person was correct; Answers from k12- hopes this helps people in the future & Good luck!

Answer 2

The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C(a+c, b), and D(c, b)

The coordinates of the midpoint of AC are ((a+c)/2, b/2)

The coordinates of the midpoint of BD are ((a+c)/2, b/2)

Explanation:

The x-coordinate of C is the addition of x-coordinates of D and B

The y-coordinate of C is the same as y-coordinates of D

The x-coordinate of the midpoint of AC are half of the distance in x-coordinate between A and C, that is, (a+c)/2

The y-coordinate of the midpoint of DB are half of the distance in y-coordinate between D and B, that is, b/2