Math Exploration 9.2

1. If you were to travel between the points (7, 3) and (-2, 4), how far would you go?

• Given: (x₁, y₁) = (7, 3) and (x₂, y₂) = (-2, 4)
• Find: d
• Concept: d² = (x₁ – x₂)² + (y₁ – y₂)²
• Solution: Use the Pythagorean Theorem to find the distance squared. Then take the square root to find the distance.
  
  • d² = (7 – -2) ² + (3 – 4) ²
  • d² = (9) ² + (-1) ² = 81 + 1 = 82
  • d = (82)^1/2 = 9.06

2. Plot the points using the graphing tool.

Figure A.9.2: The points (7, 3) and (-2, 4) are plotted using the Graphing Tool. Credit: NASA/SSU