Question

For what value of x ,the distance between the point (-2 ,5) and (x, 19) be root 205 units?
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Answer 1

Answer:

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Answer 2

Therefore the value of 'x' is 1 unit.

Given:

The distance between the points (-2,5) and (x, 19) be root 205 units.

To Find:

The value of 'x'.

Solution:

The given question can be solved as shown below.

Given that,

The distance between the points (-2,5) and (x, 19) = √205

Concept:

Let ( x₁, y₁ )and ( x₂, y₂ ) be the 2 points, then the distance between them is given by,

⇒ d = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]

Similarly, the distance between (-2,5) and (x, 19) is given by,

⇒ d = √[ ( x - (-2) )² + ( 19 - 5 ) = √205

On squaring on both sides, we get,

⇒ d = ( x + 2 )² + 14² = 205

⇒ d = ( x + 2 )² = 205 - 196 = 9

⇒ ( x + 2 ) = √9 = 3

⇒ x = 3 - 2 = 1

Therefore the value of 'x' is 1 unit.

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