Final answer:
There was a mistake in the calculation of the distance between points A(6,2) and B(1,-4) because the square root was not applied to the sum of the squared differences. The correct formula for the distance using the Pythagorean theorem is √((x2-x1)² + (y2-y1)²), resulting in the distance √61, not 61.
Step-by-step explanation:
The error in finding the distance between points A(6,2) and B(1,-4) lies in the incorrect application of the Pythagorean theorem. The correct formula to calculate the distance, denoted as AB, between two points in a Cartesian plane is AB = √((x2-x1)² + (y2-y1)²). In this case, the correct calculation should be:
- Find the differences in the x-coordinates and y-coordinates: (6-1) and (2-(-4))
- Square the differences: 5² and 6²
- Add the squared differences: 25 + 36
- Take the square root of the sum: √(25+36) = √61
The error in the original calculation was failing to take the square root of the sum, which resulted in an incorrect answer of 61 instead of the correct distance √61.