Question

Let $A(6,-1),B(1,3)$ and $C(x,8)$ be three points such that $AB=BC.$ Then the value of $x$ can be

• A. $2$
• B. $-3$
• C. $5$
• D. $1$

Answer 1

Answer: (B), (C)

The correct options are
B $-3$
C $5$

Given $AB=BC$
$\therefore (AB{)}^2=(BC{)}^2\Rightarrow (1-6{)}^2+(3-(-1){)}^2=(x-1{)}^2+(8-3{)}^2\Rightarrow 25+16=(x-1{)}^2+25\Rightarrow 16=(x-1{)}^2\Rightarrow x-1=\pm 4\therefore x=-3,5$