Question

If $(\frac{3}{2},0),(\frac{3}{2},6)$ and $(-1,6)$ are midpoints of the sides of a triangle, then find
i) centroid of the triangle,
ii)Incenter of the triangle.

Answer 1

Centroid of the triangle formed by midpoints of the sides is same as the centroid of the bigger triangle.

$(\frac{2}{3},\frac{12}{3})$

Incircle passes through the midpoints of the sides the triangle formed by these points is right angled one so we can say that its side is the diagonal , the midpoint of it is the center of the circle.

$(\frac{\frac{3}{2}-1}{2},\frac{6+0}{2})=(\frac{1}{4},3)$