Question

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

Answer 1

`\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 = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([10-(-14)]^2+[-2-(-9)]^2)\implies d=√((10+14)^2+(-2+9)^2) \\\\\\ d=√(24^2+7^2)\implies d=√(625)\implies d=25`

Answer 2

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