Q11 of 48 Page 102

If the vertices of a quadrilateral are (1, 4), (–5, 4), (–5, –3) and (1, –3), then find the type of quadrilateral.

We have A → (1, 4)


B → (–5, 4)


C → (–5, –3)


D → (1, –3)


Using the distance formula,


AB =


=


=


=6


BC =


=


=


= 7


CD =


=


=


=


= 6


DA =


=


=


= 7


The opposite sides are equal in length.


Consider the diagonals, AC and BD.


AC =


=


=


=


BD =


=


=


=


Since the diagonals are also equal, the given quadrilateral is a rectangle.


More from this chapter

All 48 →
9

If the distance between the points (3, a) and (4, 1) be then the value of a will be:

 10

If point (x, y) is at equal distance from points (2, 1) and (1, –2), then the true statement out of the following:

 12

Which figure will be obtained by joining the points (–2, 0), (2, 0), (2, 2), (0, 4), (–2, 2) in order?

 13

In what ratio does the point (3, 4) divide the line segment joining the points (1, 2) and (6, 7)?