Test Questions on Deriving the Distance Formula Using Coordinates

📚 Quick Study Guide

• 📌 The distance formula calculates the distance between two points in a coordinate plane.
• 📐 If the points are $(x_1, y_1)$ and $(x_2, y_2)$, the distance, $d$, is given by: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
• ➕ Ensure you correctly identify and substitute the $x$ and $y$ values.
• ➖ Remember to square the differences before adding them!
• ✅ The final answer is the square root of the sum.

Practice Quiz

1. What is the distance between the points (1, 2) and (4, 6)?
   1. 5
   2. 6
   3. 7
   4. 8
2. Find the distance between the points (-2, 3) and (1, -1).
   1. 3
   2. 4
   3. 5
   4. 6
3. Calculate the distance between (0, 0) and (5, 12).
   1. 12
   2. 13
   3. 14
   4. 15
4. What is the distance between the points (-3, -5) and (2, 7)?
   1. 12
   2. 13
   3. 14
   4. 15
5. Determine the distance between (4, -2) and (-1, 10).
   1. 13
   2. 14
   3. 15
   4. 16
6. Find the distance between the points (7, -4) and (7, 8).
   1. 10
   2. 11
   3. 12
   4. 13
7. Calculate the distance between (-6, 2) and (3, 2).
   1. 7
   2. 8
   3. 9
   4. 10