Use the image to answer the question.
A coordinate plane shows the x and y axes ranging from negative 6 to 6 in unit increments. Four points are plotted and labeled on the plane. The coordinates of the plotted points and the labels are as follows: left parenthesis 2 comma 1 right parenthesis is labeled as daisies, left parenthesis 5 comma 1 right parenthesis as roses, left parenthesis 5 comma 5 right parenthesis as lilies, and left parenthesis 2 comma 6 right parenthesis as sunflowers.
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.
The roses are located at (5,1) and the lilies are located at (5,5). Since the x-coordinate is the same for both points, we can see that they are both 5 feet away horizontally from the y-axis.
The y-coordinate of the roses is 1 and the y-coordinate of the lilies is 5. To find the vertical distance between the two points, we subtract the y-coordinate of the roses from the y-coordinate of the lilies: 5 - 1 = 4. Therefore, the roses are 4 feet away vertically from the lilies.
Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the horizontal and vertical distances between the two points, we can find the distance between the roses and the lilies:
a = 5 feet (horizontal distance)
b = 4 feet (vertical distance)
c = √(5^2 + 4^2) = √41
Therefore, the roses are approximately √41 feet away from the lilies on the map of the flower shop.