Question

If $A(6,-1),B(1,3)$ and $C(k,8)$ are three points such that $AB=BC$, find the value of $k$.

Answer 1

Given$A(6,-1),B(1,3)$ and $C(k,8)$

Using distance formula

$A{B}^2=B{C}^2$

$\Rightarrow (6-1{)}^2+(-1-3{)}^2=(k-1{)}^2+(8-3{)}^2$

$\Rightarrow 25+16=k^2+1-2k+25$

$\Rightarrow k^2-2k-15=0$

$\Rightarrow k^2-5k+3k-15=0$

$\Rightarrow k(k-5)+3(k-5)=0$

$\Rightarrow (k-5)(k+3)=0$

$k-5=0\Rightarrow k=5$

$k+3=0\Rightarrow k=-3$