Question

Given A(1, 5) and B(3, 13), find AB.

Answer 1

$\dag\bf\:A(x_1,y_1)=(1,5)$

$\dag\bf\:B(x_2,y_2)=(3,13)$

We have to find distance between point A and point B$.$

$\bigstar\:\boxed{\bf{AB=\sqrt{(x_2-x_1)^2+(y_2+y_1)^2}}}$

$:\implies\tt\:AB=\sqrt{(3-1)^2+(13-5)^2}$

$:\implies\tt\:AB=\sqrt{(2)^2+(8)^2}$

$:\implies\tt\:AB=\sqrt{4+64}$

$:\implies\tt\:AB=\sqrt{68}$

$:\implies\tt\:AB=\sqrt{4(17)}$

$:\implies\underline{\boxed{\bf{\red{AB=2\sqrt{17}\:unit}}}}$