Question

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

​

Answer 1

Step-by-step explanation:

given

equal distance of p from A and B

PA=PB

squaring on both side

follow the above steps

Answer 2

Let the ratio be k:k or 1:1.

P(x,y) distance from A(5,1) and B(-1,5) is equal.

So,

$\qquad \frac{x_{1} + x_{2}}{2} = \mathtt{Abscissa \; of \; P} </p><p>\\ \\</p><p></p><p>\rightarrow \quad \frac{5 - 1}{2} = x \\ \\</p><p>\rightarrow \quad x = \frac{4}{2} \quad \rightarrow \boxed{x = 2}</p><p></p><p>\\ \\</p><p></p><p>\qquad \frac{y_{1} + y_{2}}{2} = \mathtt{Ordinate \; of \; P} \\ \\</p><p>\rightarrow \quad \frac{1 + 5}{2} = y \\ \\ \rightarrow \quad y = \frac{6}{2} \quad \rightarrow \boxed{y = 3} </p><p></p><p>\\ \\</p><p></p><p>\mathtt{ To \; Prove: \; \bold{3x = 2y}}</p><p></p><p>\\ \mathtt{Putting \; value \; of \; x \; and \; y}</p><p></p><p>\\ \\</p><p></p><p>\rightarrow \quad 3 \times 2 = 2 \times 3 \\ \\ \rightarrow \quad 6 = 6 \\ \\ \bold{Hence, Proved} </p><p></p><p>$