find the possible values of b

(7,b),(-1,3); d= 2radical sign7

To find the possible values of b given the points (7,b) and (-1,3) and the distance d = 2√7, we can use the distance formula.

The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Let's substitute the given values into the distance formula:

2√7 = √((-1 - 7)^2 + (3 - b)^2)

Simplifying the equation:

4(7) = (-8)^2 + (3 - b)^2

28 = 64 + (3 - b)^2

Subtracting 64 from both sides:

-36 = (3 - b)^2

Taking the square root of both sides (considering both positive and negative roots):

±√(-36) = 3 - b

±6i = 3 - b

To get the possible values of b, we can solve the equation for b:

b = 3 - 6i or b = 3 + 6i

Therefore, the possible values of b are 3 - 6i and 3 + 6i.