Question

The point (3.5) is at a distance of 14 units from the point (x, 5). What can be the value of x?
(A) Only x= 17
(B) Only x=-17
(C) x= 17 and x=-11
(D) x=-17 and x = 11​

Answer 1

Given :-

▪ The point A(3,5) is at a distance of 14 units from the point B(x, 5)

To Find :-

▪ Value of x

Solution :-

It is given that the distance between the points is AB = 14 units. Given us the two points, x can be calculated using the distance formula.

Comparing each point with the standard form of a coordinate i.e., (x, y)

• (3,5) : x₁ = 3 ; y₁ = 5
• (x,5) : x₂ = x ; y₂ = 5

Given distance as 14 units, So

⇒ AB = √{ (x₂ - x₁)² + (y₂ - y₁)² }

Given, AB = 14 units, Squaring both sides:

⇒ 14² = (x₂ - x₁)² + (y₂ - y₁)²

⇒ 196 = (x - 3)² + (5 - 5)²

⇒ 196 = (x - 3)²

⇒ 14 = x - 3

⇒ x = 17

Hence, The value of x is 17.

∴ Option (A) is correct.