Question

If A(-2,1),B(-4,-5),C(-1,-6) and D(4,5) are vertices of a parallelogram ABCD,findvthe value of a and b. Hence find the length of its side

Answer 1

ABCD is parallelogram. It is possible only when AB || CD and AD || BC .Means slope of AB = slope of CD slope of AB = (0 - 1)/(9 +2) = -1/11 slope of CD = (a - b)/(1 - 4) = (a - b)/-3e.g., -1/11 = (a - b)/-3 3 = 11(a - b) ------(1)Similarly slope of AD = slope of BC slope of AD = (a - 1)/(1 + 2) = (a - 1)/3 slope of BC = (b - 0)/(4 - 9) = b/-5 e.g., b/-5 = (a - 1)/5 5b = -5a + 5 5(a + b) = 5 ⇒ a = 1 - b , put it in above equation 3 = 11( 1 - b - b) = 11 - 22b -8 = -22b ⇒ b = 4/11 So, a = 1 - b = 1 - 4/11 = 7/11 Hence, a = 4/11 and b = 7/11 
Similarly you can find length of BC , CD and DE by using distance formula.