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.