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.
Answer & explanation
Correct answer: option 1
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