If the distance between the points (2, –2) and (–1, x) is 5, one ofthe values of x is(A) –2 (B) 2 (C) –1 (D) 1

The distance between two points (x1, y1) and (x2, y2) in a plane is given by the formula:

d = sqrt[(x2 - x1)² + (y2 - y1)²]

Given that the distance d is 5, and the points are (2, -2) and (-1, x), we can substitute these values into the formula:

5 = sqrt[(-1 - 2)² + (x - (-2))²] 5 = sqrt[(-3)² + (x + 2)²] 5 = sqrt[9 + (x + 2)²]

Squaring both sides to get rid of the square root gives:

25 = 9 + (x + 2)² 16 = (x + 2)²

Taking the square root of both sides gives two possible solutions, since the square root of a number n is both -sqrt(n) and sqrt(n):

x + 2 = 4 or x + 2 = -4

Solving these equations gives:

x = 2 or x = -6

So the possible values of x are 2 and -6. Therefore, the correct answer is (B) 2.