---

🎓 How the Interactive Midpoint & Endpoint Calculator Works (For Students)

This colorful and interactive calculator is designed to help students learn coordinate geometry in a fun, visual, and easy-to-understand way. Whether you’re studying midpoints, endpoints, or distances in 2D or 3D space, this tool breaks it all down with step-by-step calculations and engaging visuals.

---

🧮 Step-by-Step Breakdown

1. Choose Your Calculation

Use the dropdown menu to pick what you want to calculate:

• 📍 Midpoint
• 📌 Endpoint

Then choose your coordinate type:

• 🔲 2D (x, y)
• 🧊 3D (x, y, z)

---

2. Enter Your Coordinates

Depending on the mode you choose, input:

• For midpoint: the coordinates of points A and B
• For endpoint: one endpoint and the midpoint, then solve for the missing point

The interface is mobile-friendly, stylish, and optimized for classroom or homework use.

---

3. Visualize the Math

Once you enter your values, you’ll see:

• Coordinate Plot Graph: A scatter chart shows your points and line segments in 2D or 3D.
• X vs Y Comparison Graph: Bar chart shows changes in X and Y (and Z) visually.
• Segment Ratio Chart: A visual doughnut chart displays the distances from A to Midpoint and Midpoint to B.

These visual aids make abstract math concrete and fun!

---

4. Distance Calculations

Now the calculator also shows:

• 📏 Total distance between points
• 🧮 A to Midpoint and Midpoint to B distances
• ✅ Verification: Confirms both segments are equal when using the midpoint formula
• 💡 Hover tooltips reveal exact lengths and ratios in each chart

---

5. Detailed Calculations and Proof

You’ll get:

• Step-by-step formulas with your values plugged in
• Exact decimal results
• Math proofs showing how the midpoint divides the segment equally
• ✅ Useful for checking homework or understanding the concept in depth

---

🖼️ Bonus Features

• 🎨 Colorful and modern interface with gradients and smooth animations
• 📱 Mobile responsive: Works on phones, tablets, and desktops
• 🧲 Extra tools and add-on buttons for related geometry calculators (distance, slope, etc.)

---