To find the distance between the roses and the lilies, we can use the distance formula, which is derived from the Pythagorean theorem. The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D plane is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given the coordinates:
- Lilies at (5, 5)
- Roses at (5, 1)
We can assign:
- \((x_1, y_1) = (5, 5)\) (Lilies)
- \((x_2, y_2) = (5, 1)\) (Roses)
Now, we can plug these values into the distance formula:
\[ d = \sqrt{(5 - 5)^2 + (1 - 5)^2} \] \[ d = \sqrt{(0)^2 + (-4)^2} \] \[ d = \sqrt{0 + 16} \] \[ d = \sqrt{16} \] \[ d = 4 \]
Therefore, the distance between the roses and the lilies is 4 feet.
In summary, I substituted the coordinates of the lilies and roses into the distance formula and calculated the distance to find that they are 4 feet apart.