The points A(-3,6), B(0,7) and C(1,9) are the mid points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.

ABCD is a rectangle and P,R and S are the mid - points of the AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Show that the points A(4, 7 ) B (8,4) and C(7,11) are the vertices of a right angled triangle.

Show that the point A(3,7) B(6,5) and C(5,-1) are collinear.

PQRS is a rectangle formed by joining the points P(-1, -1), Q(-1, 4), R(5,4) and S(5, -1) . A, B, C and D are the mid points of PQ, QR, RS and SR respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

In trigle ABC, the points D, E, F are the midpoints of the sides BC,CA, and AB respee. Tively. Using vector methed ,show that the area of Delta DEF is equal to (1)/(4) (area of ABC).

Show that the points A (4, 2), B (7, 5) and C (9, 7) are three points lying on a same line.

If A(-5, 7), B(-4, -5), C(-1, -6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

If A(0,1,1), B(3, 1,5) and C(0, 3, 3) are three points show that DeltaABC is right angled at C.