Question

The four vertices of a quadrilateral are (1, 2), (−5, 6), (7, −4) and (k, −2) taken in order. If the area of the quadrilateral is zero, find the value of k.

Answer 1

Let A(1, 2), B(−5, 6), C(7, −4) and (k, −2) be the given points.

Area of ΔABC

Area of ΔADC

Area of quadrilateral ABCD

= Area of ABC + Area of ADC

=(6 + 3k -15)

But are of quadrilateral= 0 (given)