Exploring Midpoints, Distance, and Line Behavior in Coordinate Geometry

I’ve been practicing coordinate geometry dash lite and wanted to create a deeper multi-part exercise focused on midpoint formulas, distance calculations, and how changing coordinates affects line behavior. I would really appreciate a detailed, step-by-step explanation for each section.

Part A:

Given two points A(1, 3) and B(7, 11):

• Calculate the midpoint of segment AB.
• Show the midpoint formula and explain how each coordinate is calculated.
• Find the distance between points A and B using the distance formula.
• Explain what the distance value represents geometrically on the coordinate plane.

Part B:

Now move point B to a new location B'(7, 3):

• Find the new midpoint between A(1, 3) and B'(7, 3).
• Calculate the distance between these two points.
• Compare the result with Part A.
• Identify what type of line segment is formed and explain how the coordinates reveal this immediately.

Part C:

Consider two new points C(4, 2) and D(4, 10):

• Calculate the midpoint of CD.
• Determine the distance between the points.
• Explain what happens when both points share the same x-coordinate.
• Describe the appearance and properties of this line on a graph.
• Discuss why the slope cannot be calculated normally in this situation.

Part D:

Finally, compare all three examples from Parts A, B, and C:

• Explain how coordinate changes affect midpoint position, distance, and line orientation.
• Describe the visual differences between diagonal, horizontal, and vertical line segments.
• Discuss how these concepts help build a stronger understanding of graph interpretation in algebra and geometry.