Question

A parallelogram has vertices P (1,4) ; Q(7,11) ; R(a,4) and S(1;-3) . find the value of a.

Answer 1

as  it is parallelogram the opposite sides are equal.

hence the distance PQ = distance SR
        
              root   (1-1)^2 + (-3-4)^2   = root (a-7)^2 + (4-11)^2

                     0 + (-7)^2   = a^2 - 14 a + 49 + (-7)^2

                               0  = a^2 - 7a - 7a  +49 

                                 0= ( a-7)   (a- 7)

                               a= 7 
hope it helps!!