Final answer:
The error in finding the distance between A(6,2) and B(1,-4) may involve incorrect application of the distance formula. The correct procedure involves subtracting the coordinates, squaring the results, summing these squares, and then taking the square root. The final distance should be a positive scalar value.
Step-by-step explanation:
The calculation of the distance between two points A(6,2) and B(1,-4) in a Cartesian plane is a fundamental concept in Mathematics, specifically in coordinate geometry. To find the distance between two points (x1, y1) and (x2, y2), we use the distance formula derived from the Pythagorean theorem:
d = √[(x2 - x1)2 + (y2 - y1)2]
Applying this formula to our points A(6,2) and B(1,-4), we get:
d = √[(1 - 6)2 + (-4 - 2)2]
d = √[(-5)2 + (-6)2]
d = √[25 + 36]
d = √[61]
d ≈ 7.81 units
This calculation yields the distance between points A and B. It is essential to square the differences and sum them before taking the square root to get the correct distance. If the student's error involved other operations (such as not squaring or incorrect subtraction), the result would be incorrect. It is also important to note that distance is a scalar quantity, which means it has magnitude but no direction, and therefore it is always positive. The negative signs that result from the subtraction within the square root are always negated by the act of squaring.