A (a + 1,a -1), B(a? +1,a?-1)and C(a? +1,a?-1) are given points D(11,9) is the mid point of AB and E (41,39) is the mid point of BC. If F is the mid point of AC then (BF)? is equal to

Hello Krishna, given A [(a +1),(a-1)] and B [(a2 +1),(a2-1)] has mid point D(11,9)
So a + 1 + a2 + 1 = 2 * 11 = 22
OR a2 + a - 20 = 0
==> a = 4 or a = - 5
Let us take a = 4
So A will become (5,3), B will be (17, 15) and C (65, 63) as C is given as [(a3+1),(a3-1)]
Hence F being mid point of AC will be [70/2 , 66/2] i.e (35,33)
So required BF2 = (35-17)2 + (33 - 15)2 = 2 * 182 = 2 * 324 = 648
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