Question

how could you use coordinate geometry to prove that \\(\overline{bd}\\) and \\(\overline{ac}\\) bisect one another?

prove the slopes are the same.
prove the slopes are opposite reciprocals.
prove the lengths are the same.
prove the midpoints are the same.

Explanation:

Define bisection in coordinate geometry

Two line segments bisect each other if and only if they share the same midpoint.

Analyze the given segments

The segments to prove bisection for are the diagonals \(\overline{BD}\) and \(\overline{AC}\).

Determine the correct coordinate proof method

To prove that \(\overline{BD}\) and \(\overline{AC}\) bisect each other, we must calculate the midpoint of \(\overline{BD}\) and the midpoint of \(\overline{AC}\) and show that they are the same point.

Answer:

• Prove the slopes are the same.
• Prove the slopes are opposite reciprocals.
• Prove the lengths are the same.
• Prove the midpoints are the same. (Correct answer)