# 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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