Question

The point whose abscissa is equal to its ordinate and which is equidistant from $A(5,0)$ and $B(0,3)$ is

• A. $(1,1)$
• B. $(2,2)$
• C. $(3,3)$
• D. $(4,4)$

Answer 1

The correct option is D $(4,4)$

Let $P(x,y)$ be the point which is equidistant from $A(5,0)$ and $B(0,3)$

Given that in $P$, abscissa is equal to ordinate i.e., $x=y$. Also it is given that $AP=BP$

$\therefore \sqrt{(x-5{)}^2+(x-0{)}^2}=\sqrt{(x-0{)}^2+(x-3{)}^2}$

Squaring on both sides

$\Rightarrow (x-5{)}^2+x^2=x^2+(x-3{)}^2$

$\Rightarrow x^2+25-10x+x^2=x^2+x^2+9-6x$

$\Rightarrow 25-10x=9-6x$

$\Rightarrow 4x=16$

$\Rightarrow x=4$

Therefore the point is $(4,4)$