Question

Find the length of the line segment between the points (-14,-9) and (10,-2).

Answer 1

d= sqrt((y2-y1)^2 +(x2-x1)^2)

  = sqrt((-2+9)^2+(10+14)^2)

   = sqrt((7^2 +24^2)

    = sqrt(49+576)

    = sqrt(625)

    = 25

Answer 2

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-14}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[10-(-14)]^2+[-2-(-9)]^2}\implies d=\sqrt{(10+14)^2+(-2+9)^2} \\\\\\ d=\sqrt{24^2+7^2}\implies d=\sqrt{625}\implies d=25$