What you’ll learn
Find distance between coordinate points.
Key idea
Coordinate changes form perpendicular right-triangle legs; straight distance is not the sum of their absolute lengths.
Straight distance uses squared coordinate changes; complete unordered point sets still must use the explicitly requested horizontal projection.
Worked example
Enter the exact value or ordered values in the format requested below.
Read A and B on this labeled grid and enter their exact straight-line distance in grid units as a number.
Marked coordinates: B=(1, 5); A=(-2, 1).
- From labeled A(-2, 1) to B(1, 5), coordinate changes are Δx=3, Δy=4.
- Distance=√((1-(-2))²+(5-(1))²)=√25=5; horizontal-then-vertical projection uses point (1, 1).
Answer: 5
Quick Check
Relate the graph used in 'Find distance between coordinate points' to an equation, table, transformation, or verbal description.
Connect the labeled A/B graph to its exact distance expression with squared-coordinate evidence.
Marked coordinates: A=(0, -2); B=(-3, -6).