Three ballet dancers are positioned on stage. If Regan is 9.4 feet straight behind Wesley and 2.2 feet directly left of Bill, how far is Wesley from Bill? If necessary, round to the nearest tenth.
___ feet
How far is Wesley from Bill?
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To find the distance between Wesley and Bill, we can visualize the positions of the dancers on a coordinate system.
1. Let’s assume Wesley is at the point (0, 0).
2. Regan is 9.4 feet directly behind Wesley, which places Regan at (0, -9.4).
3. Regan is also 2.2 feet directly left of Bill, meaning Bill must be at the point (2.2, -9.4) since moving left involves adding to the x-coordinate.
Now, we want to find the distance between Wesley (0, 0) and Bill (2.2, -9.4). We can use the distance formula:
[
d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
Substituting in our values:
– (x_1 = 0), (y_1 = 0)
– (x_2 = 2.2), (y_2 = -9.4)
Calculating gives us:
[
d = sqrt{(2.2 – 0)^2 + (-9.4 – 0)^2}
]
[
d = sqrt{(2.2)^2 + (-9.4)^2}
]
[
d = sqrt{4.84 + 88.36}
]
[
d