If the distance between the points (x, -1) and (3, 2) is 5 units, then what will be the value of x.

Concept -

The distance between two points  and  in a 2D plane is given by the distance formula:

Explanation -

Here, the points are (x, -1) and (3, 2), and the distance is given as 5 units. Using the distance formula:

let's square both sides to eliminate the square root:

Now, take the square root of both sides:

Solve for x in both cases:

When 3 - x = 4:
x = 3 - 4 
 x = -1 

When 3 - x = -4:
 x = 3 + 4 
 x = 7 

So, the values for x are x = -1 or x = 7.