If the points A(6, 1), B(8, 2), C(9, 4) and D(7, k) are the vertices of a parallelogram taken in order, then find the value of k.

3

Distance between A and B = \(\sqrt {( 8-6)² + (2-1)²}\)

= \(\sqrt {4+ 1}\)

= \(\sqrt {5}\)

Distance between B and C = \(\sqrt {( 9-8)² + (4-2)²}\)

= \(\sqrt {1+ 4}\)

= \(\sqrt {5}\)

As , Opposite side of parllelogram is of equal length so, BC = AD

( \(\sqrt {5}\) )² = \(\sqrt {( 7-6)² + (k-1)²}\)

On squaring both side

5 = 1 + (k-1)²

4 = (k-1)² 

K = 2 + 1 = 3

Answer :- 3