Question

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

Answer 1

2.899

Explanation:

The formula for calculating the distance between two points P(x1, y1) and (x2, y2) is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the points (2,-2) and (1,x) and the distance between the point as 5, we are to get x. To get x we will substitute the points and the distance given into the formula.

Given x1 = 2, y1 = -2, x2 = 1, y2 = x and D = 5

On substitution:

5 = √(1-2)²+(x-(-2))²

5 = √1²+(x+2)²

5 = √1+(x+2)²

Square both sides of the equation

5² = (√1+(x+2)²)²

25 = 1+(x+2)²

(x+2)² = 25-1

(x+2)² = 24

Square both sides

√(x+2)² = √24

x+2 = √24

x = √24- 2

x = 4.899-2

x = 2.899

Hence the other value is 2.899