Question

If A = (7, 9) and B = (3, 12), what is the length of AB

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{9})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(3-7)^2+(12-9)^2}\implies AB=\sqrt{(-4)^2+3^2} \\\\\\ AB=\sqrt{16+9}\implies AB=\sqrt{25}\implies AB=5$

Answer 2

The Pythagorean theorem is used to find the distance between two points. If that distance is "c", it satisfies the relation

... a² + b² = c²

where "a" and "b" are the horizontal and vertical differences between the point coordinates. Here,

... a = 7 - 3 = 4 . . . . horizontal difference

... b = 12 - 9 = 3 . . . . vertical difference

Then we have

... 4² + 3² = c² = 25

... c = √25 = 5

The length of AB is 5 units.