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 1

ANSWER

A(5,1)≡(x

1

,y

1

)

B(−1,5)≡(x

2

,y

2

)

P≡(x,y)

PA=PB ....(given)

∴ By distance formula

(x−x

1

)

2

+(y−y

1

)

2

we have,

⇒(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

∴−2y+10y=2x+10x

∴8y=12y

2y=3x. [henceproved

option-2ok

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Answer 2

Answer:

3x = 2y or 2y = 3x

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  

  Correct option is C