Question

$AB$ is a line segment of length $24$ cm. $P$ is a point on $AB$ such that $A{P}^2+P{B}^2$ is minimum, then $AP=$

• A. $12$
• B. $6$
• C. $18$
• D. $24$

Answer 1

Answer: (A)

$12$

Let $AP=x$

Thus $PB=24-x$

We know $f\left(x\right)=A{P}^2+P{B}^2=x^2+(24-x{)}^2$

$f^{\prime }\left(x\right)=2x-2(24-x)=0$

$\Rightarrow 2\times 24=4x$

$\Rightarrow x=12$