Question 949147
{{{drawing(300,300,-6,6,-6,6,grid(1),circle(-1,-2,0.3),circle(5,4,0.3),circle(-3,0,0.3),line(-1,-2,5,4),line(5,4,-3,0),line(-3,0,-1,-2))}}}
Find the distance between the points.
{{{D[1]^2=(-1-5)^2+(-2-4)^2=36+36=72}}}
{{{D[2]^2=(5-(-3))^2+(4-0)^2=64+16=80}}}
{{{D[3]^2=(-3-(-1))^2+(0-(-2))^2=4+4=8}}}
If it's a right triangle, it follows the Pythagorean theorem,
{{{72+8=80}}}
{{{80=80}}}
True, so it is a right triangle.
.
.
{{{A=(1/2)bh=(1/2)(sqrt(72))(sqrt(8))=(1/2)sqrt(576)=(1/2)(24)=highlight(12)}}}