Q4 of 149 Page 14

Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.

We know if the quadrilateral is parallelogram if opposite sides are equal.


Let our points be A(3, -2), B(4, 0), C(6, -3) and D(5, -5).



By distance formula,


XY =


For AB,


AB =


=


= units


For BC,


BC =


=


= units


For CD,


CD =


=


= units


For AD,


AD =


=


= units


Here, we observe that AB = CD and AD = BC, which means that the quadrilateral formed by lines joining by points, is parallelogram.


More from this chapter

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2

Find the points of trisection of the line segment joining the points:

(i) (5, -6) and (- 7, 5), (ii) (3, -2) and (-3, -4), (iii) (2, -2) and (-7, 4)

 3

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and (1, 2) meet.

 5

Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex

 6

The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.