﻿ A(a + 1, a – 1), B(a2 + 1, a2 – 1) and C(a3 + 1, a3 – 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 the (BF)2 is equal to : Kaysons Education

# A(a + 1, a – 1), B(a2 + 1, a2 – 1) And C(a3 + 1, a3 – 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 the (BF)2 is Equal To

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## Question

### Solution

Correct option is

648

We have

⇒ a + a2 – 20 = 0 ⇒ a = –5 or 4

⇒ a2 + a3 = 80 which holds for a = 4.

So, the given points are A(5, 3), B(17, 15), C(65, 63) and

Coordinates of F are  and

(BF)2 = (35 – 17)2 + (33 – 15)2

= (18)2 + (18)2 = 648

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