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Complete the coordinate proof of the theorem.


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

The coordinates of the midpoint of AC¯¯¯¯¯ are ( , b2).

The coordinates of the midpoint of BD¯¯¯¯¯ are (a2, ).

The midpoints of the diagonals have the same coordinates.

Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.

Complete the coordinate proof of the theoremThe coordinates of parallelogram ABCD are A 0 0 B a 0 C and D 0 bThe coordinates of the midpoint of AC are b2The coo class=
Complete the coordinate proof of the theoremThe coordinates of parallelogram ABCD are A 0 0 B a 0 C and D 0 bThe coordinates of the midpoint of AC are b2The coo class=


Answer :

From the given coordinates, we can say that the Midpoint of AC = a/2, b/2 and the Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

What is the coordinate of the midpoint?

From the given image, we see that the coordinates of parallelogram ABCD are;

A (0, 0)

B (a, 0)

C (a , b)

D (0, b)

Thus;

1) The coordinates of the midpoint of AC are;

Midpoint of AC = (0 + a)/2, (0 + b)/2

Midpoint of AC = a/2, b/2

2) The coordinates of the midpoint of BD are;

Midpoint of BD = (a + 0)/2, (0 + b)/2

Midpoint of BD = a/2, b/2

Since the midpoints of the diagonals have the same coordinates, then we can conclude that AC and BD bisect each other.

Read more about Coordinate of Midpoint at; https://brainly.com/question/5566419

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