Question

if the point Q (x, y) is equidistant from R(5, 1) and S(-1, 5), then which of the following Statment is correct​

Answer 1

Question: if the point Q (x, y) is equidistant from R(5, 1) and S(-1, 5), then which of the following statement is correct:

a.)3x=4y b.)x=2y c.)3x=2y

d.)x=3y​

Answer:

3x = 2y

Step-by-step explanation:

Using distance formula, distance b/w points (x₁, y₁) , (x₂, y₂) is given by √(x₁ - x₂)² + (y₁ - y₂)².  In the question:

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

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

⇒ - 2y - 10x = 2x - 10y

⇒ -2y + 10y = 2x + 10x

⇒ 8y = 12x

⇒ 2y = 3x