Question

Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the following could be used to calculate the coordinates for point B?
5 = square root of the quantity of x minus 6 all squared plus y minus 5 all squared
5 = square root of the quantity of x minus 5 all squared plus y minus 6 all squared
5 = square root of the quantity of x plus 6 all squared plus y plus 5 all squared
5 = square root of the quantity of x plus 5 all squared plus y plus 6 all squared

Answer 1

The distance between (x1, y1) and (x2, y2) is found using the Pythagorean theorem. It is ...

$\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

For your values of (x1, y1) = (6, 5) and d = 5, substituting into the formula gives

$\displaystyle 5=\sqrt{(x-6)^2+(y-5)^2}$

This matches the first selection.