Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A cartographer is marking locations on a grid. Point A is at (3, 7) and Point B is at (9, 15). What is the distance between Point A and Point B?
- A√68
- B√100
- C10
- D√164
Show answer & explanationAnswer & explanation
Correct answer: C. 10
Use the distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²). Here, x₁=3, y₁=7, x₂=9, y₂=15. So, d = √((9-3)² + (15-7)²) = √((6)² + (8)²) = √(36 + 64) = √100 = 10.
Why the other options are wrong
- A. This results from √((9-3)² + (15-7)²) = √(6² + 8²) = √(36 + 64) = √100, if an error was made in calculation.
- B. This is √100, which simplifies to 10. The instruction is to simplify if possible.
- D. This is the result of adding the squared differences, but with an error in calculation or forgetting the square root.
Distance Formula
The distance formula calculates the length of a line segment between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane.
- Derived from the Pythagorean theorem.
- Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).
- Always yields a non-negative value.
Memory trick: Coordinates are far when you square the differences, add, then root.