Q16 of 112 Page 156

Show that the opposite sides of a quadrilateral with vertices A (–2, –4), B (5, –1), C (6, 4) and D (–1, 1) taken in order are parallel.

Let A (–2, 2), B (1, 2), C (–1, –3) and D (–4, –3) be the given points taken in order.



Now,


Slope of line passing through (x1, y1) and (x2, y2) is



Slope of AB




Slope of CD =




∴ Slope of AB = Slope of CD


Hence, AB is parallel to CD. … (1)


Now,


Slope of BC




Slope of AD =





∴ Slope of BC = Slope of AD


Hence, BC is parallel to AD. … (2)


From (1) and (2), we see that opposite sides of quadrilateral are parallel.


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