Question

Find x so that the Distance between the two points (x,3) and (-2,5) is 8.

Answer 1

The distance between given points are 5.74

Explanation:

Given as :

The Distance of line = 8

The points which join the line is ( x , 3 ) And ( - 2 , 5 )

So, From distance formula

Distance =
`\sqrt{(x_2-x_1)^(2) + (y_2-y_1)^(2)}`

Or, 8 =
`\sqrt{( - 2- x)^(2) + (5 - 3)^(2)}`

Or, 8² = (- x - 2)² + 2²

Or, 64 - 4 = (-1)²(x + 2)²

Or 60 = x² + 4x + 4

Or, x² + 4x - 56 = 0

Or x =
`\frac{-b\pm \sqrt{(b^(2)-4* a* c)}}{2a}`

So, x =
`\frac{-4\pm \sqrt{(4^(2)-4* 1* (-56))}}{2a}`

Or, x =
`(-16\pm √(240))/(2)`

So, x = 5.74 , - 9.74

Hence The distance between given points are 5.74 Answer