How do I find the distance between two points (3, 4) and (7, 1)?
I know there is a distance formula but I cannot remember it properly. Also, can you explain why the formula works (the geometric proof)?
1 Answer
KKKavya Krishnan
✓ Accepted
· 14d ago
▲ 5
Distance = sqrt((x2-x1)^2 + (y2-y1)^2). For (3,4) and (7,1): d = sqrt((7-3)^2 + (1-4)^2) = sqrt(16 + 9) = sqrt(25) = 5. The proof: draw a right triangle where the hypotenuse is the distance between the points. The horizontal leg = |x2-x1| = 4 and vertical leg = |y2-y1| = 3. By Pythagoras: d^2 = 4^2 + 3^2 = 25, so d = 5. This is a classic 3-4-5 Pythagorean triple.
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