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

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]

Here, we are given that the distance d = 5, x1 = 2, y1 = -2, x2 = -1, and we need to find the value of y2 which is represented as x in the question.

Substituting the given values into the formula, we get:

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, we get:

25 = 9 + (x + 2)² 16 = (x + 2)²

Taking the square root of both sides, we get:

±4 = x + 2

Solving for x, we get two possible values:

x = 4 - 2 = 2 x = -4 - 2 = -6

So, the possible values for x are 2 and -6.

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

5 = sqrt[(-1 - 2)² + (x - (-2))²] 25 = (3)² + (x + 2)² 25 = 9 + x² + 4x + 4 25 = x² + 4x + 13 0 = x² + 4x - 12

This is a quadratic equation in the form ax² + bx + c = 0, where a = 1, b = 4, and c = -12. We can solve for x using the quadratic formula:

x = [-b ± sqrt(b² - 4ac)] / 2a x = [-4 ± sqrt((4)² - 41(-12))] / 2*1 x = [-4 ± sqrt(16 + 48)] / 2 x = [-4 ± sqrt(64)] / 2 x = [-4 ± 8] / 2

So the possible values for x are x = 2 or x = -6.