Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A geometer is analyzing a line segment on a coordinate plane. The segment connects point A (2, 5) and point B (8, 1). What is the length of this line segment?
- A√52 units
- B√68 units
- C√40 units
- D√32 units
Show answer & explanationAnswer & explanation
Correct answer: A. √52 units
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by the distance formula: d = √((x2 - x1)² + (y2 - y1)²). For points A(2, 5) and B(8, 1): d = √((8 - 2)² + (1 - 5)²) = √((6)² + (-4)²) = √(36 + 16) = √52 units.
Why the other options are wrong
- B. Incorrect calculation; this would be (8-0)^2 + (1-0)^2 if from origin.
- C. Incorrect calculation; perhaps (8-2)^2 + (1+5)^2 = 36+36=72.
- D. Incorrect calculation; (8-2)^2 + (5-1)^2 = 36 + 16 = 52.
Distance Formula (Coordinate Geometry)
A formula used to find the distance between two points in a Cartesian coordinate system.
- Derived from the Pythagorean theorem.
- Formula: d = √((x2 - x1)² + (y2 - y1)²).
- The order of (x1,y1) and (x2,y2) does not affect the final distance.
Memory trick: X difference squared, Y difference squared, add them, root them, distance is shared!