label the points
A(-3,1) , B(3,-1) and C(1,3)
AB = β(6^2 + (-2)^2) = β40
BC= β(2^2 + 4^2) = β20
AC = β(4^2 + 2^2) = β20
Two of the sides are equal so the triangle is isosceles.
here is a quick way to find the area if you are given the 3 points.
list the coordinates in a column, repeating the first point
-3 1
3 -1
1 3
-3 1
area = (1/2) | downproducts - upproducts|
= (1/2) |3+9+1 - (3-1-9)|
= (1/2)|13 +7|
= 10
or use Heron's Formula
Area = β(s(s-a)(s-b)(s-c)) , where a, b, and c are the sides and s = (1/2) the perimeter
s = (β40 + 2β20)/2 = (2β10 + 4β5)/2 = β10 + 2β5
s-a = β10 + 2β5 - 2β5 = β10
s-b = β10 + 2β5 - 2β5 = β10
s-c = β10 + 2β5 - 2β10 = 2β5 - β10
area = β(β10+2β5)(β10)(β10)(2β5-β10)
= β10(20-10)
= 10