Question

If distance between A (2,7) and B (x,-5) is 2√37 unit, find x :-

(i) 4
(ii) -4
(iii) √2
(iv) - √2​

Answer 1

Answer:

4

Step-by-step explanation:

(x-2)² + (12)² = 4×37

x²=4x

x=4

Answer 2

Answer:

Option i) 4

Step-by-step-explanation:

The given points are

• A ≡ ( 2, 7 ) ≡ ( x₁, y₁ )
• B ≡ ( x, - 5 ) ≡ ( x₂, y₂ )

We have given that the distance between these two points is 2 √37 units.

We have to find x.

Now, by distance formula,

d ( A, B ) = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]

⇒ 2 √37 = √{ ( 2 - x )² + [ 7 - ( - 5 ) ]² }

⇒ ( 2 √37 )² = ( √{ ( 2 - x )² + [ 7 - ( - 5 ) ]² } )²

⇒ 4 * 37 = ( 2 - x )² + [ 7 - ( - 5 ) ]²

⇒ 148 = 2² - 2 * 2 * x + x² + ( 7 + 5 )²

⇒ 148 = 4 - 4x + x² + ( 12 )²

⇒ x² - 4x + 4 + 144 = 148

⇒ x² - 4x + 4 = 148 - 144

⇒ x² - 4x + 4 = 4

⇒ x² - 4x = 0

⇒ x ( x - 4 ) = 0

⇒ x = 0 OR x - 4 = 0

⇒ x = 0 OR x = 4

∴ The value of x is 0 or 4.