1. Tardigrade
  2. Question
  3. Mathematics
  4. The ABCD is a square with sides of unit length. Points E and F are taken on sides AB and AD respectively so that AE = AF. Let P be a point inside the square ABCD. The value of ( PA )2-( PB )2+( PC )2-( PD )2 is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The $ABCD$ is a square with sides of unit length. Points $E$ and $F$ are taken on sides $AB$ and $AD$ respectively so that $AE = AF$. Let $P$ be a point inside the square $ABCD$.
The value of $( PA )^{2}-( PB )^{2}+( PC )^{2}-( PD )^{2}$ is equal to

Straight Lines

Solution:

$(P A)^{2}-(P B)^{2}+(P C)^{2}-(P D)^{2}$
$=\left(\alpha^{2}+\gamma^{2}\right) \left(\alpha^{2}+\delta^{2}\right)+\left(\delta^{2}+\beta^{2}\right)-\left(\gamma^{2}+\beta^{2}\right)=0$

Solution Image