Question

if A(x,y) is equidistant from (-4,3) and (3,-4), show that x=y

Answer 1

Since the point A(x,y) is equidistant from the points (-4,3) and (3,-4)

It means that the distance between the point A and (-4,3) is equal to the distance between the point A and (3,-4).

To prove : x=y

By using the distance formula which states,

That the distance between the two points say $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is calculated by $\sqrt{{(x_{2}-x_{1})^{2}}+(y_{2}-y_{1})^{2}}$

Distance between (x,y) and (-4,3)= Distance between (x,y) and (3,-4)

$\sqrt{{(-4-x)^{2}}+(3-y)^{2}}=\sqrt{{(3-x)^{2}}+(-4-y)^{2}}$

Squaring on both the sides of the given equation,

${{(4+x)^{2}}+(3-y)^{2}}={{(3-x)^{2}}+(4+y)^{2}}$

$16+x^{2}+8x+9+y^{2}-6y=9+x^{2}-6x+16+y^{2}+8y$

$14x=14y$

x=y

Hence, proved.