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

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

TO FIND: value of k

PROOF: Let four vertices of quadrilateral are A (1, 2) and B (−5, 6) and C (7, −4) and D (k, −2)

We know area of triangle formed by three points is given by

Now Area of ΔABC

Taking three points when A (1, 2) and B (−5, 6) and C (7, −4)

Also,

Now Area of ΔACD

Taking three points when A (1, 2) and C (7, −4) and D (k, −2)

Hence