Question

andy and amelia were arguing about the distance formula. andy said that order matters when subtracting the xs and ys. if you dont follow the order in the formula, the answer will be the wrong sign. amelia said order doesnt really matter and you will get the same answer regardless of order of subtraction.
who is correct? why?
amelia is correct because order never matters in subtraction.
neither are correct
andy is correct because order always matters in subtraction.
amelia is correct because squaring the differences will result in a positive regardless of subtraction order.

Explanation:

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). When we square \((x_2 - x_1)\) and \((y_2 - y_1)\), for example, \((a - b)^2=a^{2}-2ab + b^{2}\) and \((b - a)^2=b^{2}-2ba+a^{2}\), so \((a - b)^2=(b - a)^2\). The sign of the difference \((x_2 - x_1)\) or \((y_2 - y_1)\) does not matter after squaring.

Answer:

Amelia is correct because squaring the differences will result in a positive regardless of subtraction order.