It will be a triangle
Calculating sides of this triangle
A(1,1)
B(8,1)
C(5,5)
side a-AB=\(\sqrt{(8-1)^{2}+( 1-1)^{2} ) }= \sqrt{ 7^{2} }=7\)
side b-AC=\(\sqrt{(5-1)^{2}+( 5-1)^{2} ) }= \sqrt{ 4^{2}+4^{2} }=[tex] \sqrt{36}\)=6 [/tex]
side c-BC=\(\sqrt{(5-8)^{2}+( 5-1)^{2} ) }= \sqrt{ (-3)^{2}+4^{2} }=[tex] \sqrt{25}\)=5 [/tex]
Area of the triangle from Herone formula:
A=\(\sqrt{p(p-a)(p-b)(p-c)}\)
p=\(\frac{1}{2}(a+b+c)\)=\(\frac{1}{2}(7+6+5)\)=9
A=\(\sqrt{9(9-7)(9-6)(9-5)}\)=\(\sqrt{9*2*3*4}\)=\(\sqrt{216}\)
Area is \(\sqrt{216}\)
