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)

1 answer

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.