Question

Find x if the distance between the points x, 2 and 3, 4 is root 8 units

Answer 1

hope it help you dear.....

Answer 2

The value of x for point A is x = 3 + 2√15  or  x = 3 - 2√15

Given: points A(x, 2) and B(3, 4).

The distance between points A and B is 8 units

To Find: The abscissa or x-coordinate of point A

Solution:

We can find the solution by applying the formula,

AB² = ( x2 - x1 )² + ( y2 - y1 )²

where ( x1 , y1 ) are coordinates of first point and ( x2 , y2 ) are coordinates of second point.

Framing our question where A(x, 2) and B(3, 4) and AB=8 units according to (1), we get

⇒ 8² =  ( 3 - x )² + ( 4 - 2 )²

⇒  ( 3 - x )² = 60

⇒ 9 + x² - 6x - 60 = 0

⇒ x² - 6x - 51 = 0

The equation (1) cannot be prime factorised so we use Sridhar Acharya formula here which states,

      x = ( - b ± √ ( b² - 4ac )) / 2a

   ∴ x = ( 6 ± √( 36 + 204 )) / 2

 ⇒  x = ( 6 ± 4√15) / 2

 ⇒  x = (3 ± 2√15)

So x = 3 + 2√15  or  x = 3 - 2√15

Hence, the value of x for point A is x = 3 + 2√15  or  x = 3 - 2√15

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