A triangle #hat(ABC)# has vertices of #A(1,3);B(1/2,3/2);C(2,1)#. Verify that the triangle is isosceles and calculate the area and perimeter?
Let us first verify that the given points are non-collinear.
We use the following necessary and sufficient condition for
collinearity of the points :
Thus, the points are not collinear, and, hence, form
Knowing that, the Area of
The Reqd. Area =
Using the Distance Formula, we have,