Q20 of 184 Page 10

If the area of the quadrilateral whose angular points taken in order are (1, 2), (-5, 6), (7, -4) and (h, -2) be zero, show that h=3.

Given: vertices of the quadrilateral be A(1, 2), B(-5, 6), C(7, -4) and D(h, -2).


Let join AC to form two triangles,


Now, We know that


Area of triangle =


Then,


Area of triangle ABC =


=


=


= 6 sq units


Now, Area of triangle ADC =


=


=


= 3h - 15


Area of quadrilateral ABCD = Area of triangle ABC+ Area of triangle ADC


= 3h – 15 + 6


= 3h = 9


= h = 3


Hence, h is 3


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