Q13 of 169 Page 644

Show that A(1, -2), B(3, 6), C(5, 10) and D(3, 2) are the vertices of a parallelogram.


Given: Vertices of the quadrilateral are A(1, -2), B(3, 6), C(5, 10) and D(3, 2).


Note: For a quadrilateral to be a parallelogram opposite sides of the quadrilateral must be equal in length, and the diagonals must not be equal.


AB


= 2√17 units


BC


= 2√5 units


CD


= 2√17 units


DA


= 2√5 units


Therefore, AB = CD and BC = DA …..(1)


AC


= 4√10 units


BD


= 4 units


Therefore, AC BD …..(2)


From 1 and 2, we have


Opposite sides of ABCD are equal, and diagonals are not equal. Hence, points A, B, C and D are the vertices of a parallelogram.


More from this chapter

All 169 →
11

Show that the points A(2, -2), B(8, 4), C(5, 7) and D(-1, 1) are the angular points of a rectangle.

 12

Show that A(3, 2), B(0, 5), C(-3, 2) and D(0, -1) are the vertices of a square.

 14

Show that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus.

 15

If the points A (-2, -1), B(1, 0), C(x, 3) and D(1, y) are the vertices of a parallelogram, find the values of x and y.