Question

Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are

• A. 44625
• B. -3, 5
• C. 3, -5
• D. 44656

Answer 1

Answer: (B)

-3, 5

Answer 2

The correct answer is B:(-3,5)
We have, $A(6,-1), B(1,3), C(x, 8)$
Also, $A B=B C$
$\Rightarrow A B^{2}=B C^{2}$
$\Rightarrow (1-6)^{2}+(3+1)^{2}=(x-1)^{2}+(8-3)^{2}$
$\Rightarrow 25+16=(x-1)^{2}+25$
$\Rightarrow (x-1)^{2}=16$
$\Rightarrow x-1=\pm 4$
$\Rightarrow x=1 \pm 4$
$\Rightarrow x=5,-3$