Question 632394
a = distance between B and C = {{{sqrt((-4-(-1))^2 + (-2-4)^2) = sqrt(45) }}}
b = distance between A and C = {{{sqrt((-4-5)^2 + (-2-1)^2) = sqrt(90)}}}
c = distance between A and B = {{{sqrt((-1-5)^2 + (4-1)^2) = sqrt(45)}}}

Therefore {{{a^2 + c^2 = b^2}}} because {{{(sqrt(45))^2 + (sqrt(45))^2 = (sqrt(90))^2}}}.

The sides satisfy the Pythagorean Theorem, therefore triangle ABC is a right triangle with angle B as a right angle.

the area is equal to
{{{A = (base)(height)/2}}}
{{{A = (sqrt(45))(sqrt(45))/2}}}
{{{highlight(A = 22.5)}}} square units