For the three points A(2,0),B(0,2),and P(1,1) | vedclass

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(C) Let the equation of the variable line passing through $P(1,1)$ be $a(x-1) + b(y-1) = 0$,which simplifies to $ax + by - (a+b) = 0$. The algebraic s

Vedclass · Accepted Answer

$d = 0$ for all lines

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(C) Let the equation of the variable line passing through $P(1,1)$ be $a(x-1) + b(y-1) = 0$,which simplifies to $ax + by - (a+b) = 0$. The algebraic sum of the distances of $A(2,0)$ and $B(0,2)$ from the line $ax + by - (a+b) = 0$ is given by: $d = \frac{a(2) + b(0) - (a+b)}{\sqrt{a^2+b^2}} + \frac{a(0) + b(2) - (a+b)}{\sqrt{a^2+b^2}}$ $d = \frac{2a - a - b}{\sqrt{a^2+b^2}} + \frac{2b - a - b}{\sqrt{a^2+b^2}}$ $d = \frac{a - b}{\sqrt{a^2+b^2}} + \frac{b - a}{\sqrt{a^2+b^2}}$ $d = \frac{a - b + b - a}{\sqrt{a^2+b^2}} = 0$. Thus,$d = 0$ for all lines passing through $P(1,1)$.

For the three points $A(2,0)$,$B(0,2)$,and $P(1,1)$,suppose $d$ is the algebraic sum of the distances of $A$ and $B$ from a line that passes through $P$. Then,which of the following is correct?

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