Question
Given:
Sunflower (2,6)
Lilies (5,5)
Daisies (2,1)
Roses (5,1)
A map of a flower shop is shown. Each coordinate represents one foot. How far are the roses from the lilies? Explain how you found your answer.
(2 points)
Sunflower (2,6)
Lilies (5,5)
Daisies (2,1)
Roses (5,1)
A map of a flower shop is shown. Each coordinate represents one foot. How far are the roses from the lilies? Explain how you found your answer.
(2 points)
Answers
GPT-4o mini
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.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
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.