ACT (Enhanced)MathematicsMedium
A meteorologist is tracking a storm. The storm's path can be approximated by a line segment between two points on a coordinate plane: (2, 5) and (8, 13). What is the length of this storm's path?
- A12 units
- B14 units
- C8 units
- D10 units
Show answer & explanationAnswer & explanation
Correct answer: D. 10 units
Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²). Here, (x1, y1) = (2, 5) and (x2, y2) = (8, 13). So, d = √((8 - 2)² + (13 - 5)²) = √((6)² + (8)²) = √(36 + 64) = √(100) = 10 units.
Why the other options are wrong
- A. Incorrect calculation, perhaps a Pythagorean triple error or wrong sum.
- B. Incorrect calculation, possibly adding the coordinate differences directly.
- C. Incorrect calculation, possibly only considering one coordinate difference or a miscalculation.
Distance Formula
The formula used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).
- Derived from the Pythagorean theorem.
- Always yields a non-negative value.
- Used for finding lengths of segments, perimeters, etc.
Memory trick: Coordinate geometry plots points like a map, and formulas measure the way.