GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A surveyor is mapping a plot of land. Point A is at coordinates (2, 3) and Point B is at coordinates (5, 7). What is the straight-line distance between Point A and Point B?
- A7 units
- B3 units
- C5 units
- D4 units
Show answer & explanationAnswer & explanation
Correct answer: C. 5 units
Use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. Here, x₁=2, y₁=3, x₂=5, y₂=7. So, d = √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √[9 + 16] = √25 = 5 units.
Why the other options are wrong
- A. This is the sum of the differences in x and y coordinates (3+4=7).
- B. This is the difference in x-coordinates (5-2=3).
- D. This is the difference in y-coordinates (7-3=4).
Distance Formula
A formula derived from the Pythagorean theorem, used to find the distance between two points in a coordinate plane.
- Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²].
- Essentially, it finds the hypotenuse of a right triangle formed by the two points.
- Used in coordinate geometry to measure lengths.
Memory trick: Distance formula is like Pythagorean theorem for maps.