Question

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Answer 1

Given :-

• The point P(x, y) is equidistant from the points A(5, 1) and B(-1, 5).

To Prove :-

• 3x = 2y

Solution :-

As P is equidistant from A and B

So,

AP = BP

From distance formula

⇒ √{(x - 5)² + (y - 1)²} = √{(x + 1)² + (y - 5)²}

⇒ (x - 5)² + (y - 1)² = (x + 1)² + (y - 5)² [ by squaring both sides ]

⇒ x² - 10x + 25 + y² - 2y + 1 = x² + 2x + 1 + y² - 10y + 25

⇒ - 10x - 2x = 2x - 10y

⇒ - 12y = - 8y

⇒ 12x = 8y

⇒ 3x = 2y

Hence, proved !

Answer 2

Step-by-step explanation:

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