#### Question If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.

#### Video Explanation

#### Explanatory Answer

Distance between two points whose coordinates are (x_{1}, y_{1}) and (x_{2}, y_{2}) = \\sqrt {{({{x}_{2}}-{{x}_{1}})}^{2}+{({{y}_{2}}-{{y}_{1}})}^{2}})

##### Given information

Distance between P(x, y) and A(5, 1) = distance between P(x, y) and B(-1, 5)

Distance between P and A = \\sqrt {{(x-5)}^{2}+{(y-1)}^{2}})

Distance between P and B = \\sqrt {{(x+1)}^{2}+{(y-5)}^{2}})

Equate the two distances and solve for x and y.

\\sqrt {{(x-5)}^{2}+{(y-1)}^{2}}) = \\sqrt {{(x+1)}^{2}+{(y-5)}^{2}})

Square both the sides of the equation

(x – 5)^{2} + (y - 1)^{2} = (x + 1)^{2} + (y – 5)^{2}

x^{2} – 10x + 25 + y^{2} – 2y + 1 = x^{2} + 2x + 1 + y^{2} – 10y + 25

-12x = -8y

Or 12x = 8y

Or 3x = 2y