Question

What is the distance between the points (1,-6) and (-5,2)

A 5.6 units

B 7.2 units

C 9 units

D 10 units



Question two is shown in picture answer both plz thanks

Answer 1

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{2})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([-5-1]^2+[2-(-6)]^2)\implies d=√((-5-1)^2+(2+6)^2) \\\\\\ d=√((-6)^2+8^2)\implies d=√(36+64)\implies d=√(100)\implies d=10 \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{9})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ AB=√([-1-(-3)]^2+[6-9]^2)\implies AB=√((-1+3)^2+(6-9)^2) \\\\\\ AB=√(2^2+(-3)^2)\implies AB=√(13)\implies AB\approx 3.6`