If the distance between (b, 3) and (7, 3) is 3.5 units, find all possible values of b.
Or, you can stop at:
3.5^2 = (3 - 3)^2 + (7 - b)^2
and you have
(b-7)^2 = 3.5^2
b-7 = ±3.5
b = 7±3.5
or, you can notice that they lie on the same horizontal line, so (b,3) is either 3.5 units to the right or to the left of (7,3)
so b = 7 ± 3.5
which is what Steve shows in his last line as well.
To find all possible values of b, we can use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the distance between (b, 3) and (7, 3) is given as 3.5 units:
3.5 = √((7 - b)^2 + (3 - 3)^2)
Simplifying the equation, we get:
12.25 = (7 - b)^2
Taking the square root and solving for (7 - b), we have:
√12.25 = 7 - b
±3.5 = 7 - b
To find the possible values of b, we can solve for both cases:
1. Case 1: 3.5 = 7 - b
Subtracting 7 from both sides:
-3.5 = -b
Multiplying by -1:
3.5 = b
2. Case 2: -3.5 = 7 - b
Adding 3.5 to both sides:
3.5 = 7 - b
Subtracting 7 from both sides:
-3.5 = -b
Multiplying by -1:
3.5 = b
Therefore, the possible values of b are 3.5 or -3.5.
Use the distance formula:
d^2 = (y2 - y1)^2 + (x2 - x1)^2
where
d = distance
(x1, y1) and (x2, y2) = points
Thus,
3.5^2 = (3 - 3)^2 + (7 - b)^2
12.25 = 0 + 49 - 14b + b^2
Now solve for b.