Question

Mandy created a treasure hunt in the sand at the beach. To keep track of where she buried four items, she graphed their locations on the coordinate plane. The coordinates for each item are as follows:

Item 1: (2, 15)
Item 2: (15, -5)

What are the coordinates of Item 3? Explain how you found its coordinates. Be sure to explain how you identified the sign of each coordinate.

Answer 1

The predicted coordinates of Item 3 are (28, -25).

Explanation:

To determine the coordinates of Item 3, we need to analyze the pattern between the coordinates of Item 1 and Item 2.

Item 1: (2, 15)

Item 2: (15, -5)

Observing the x-coordinates, we notice that Item 2's x-coordinate (15) is 13 units more than Item 1's x-coordinate (2).

This indicates a consistent increase of 13 units in the x-coordinates.

Now, let's examine the y-coordinates. Item 2's y-coordinate (-5) is 20 units less than Item 1's y-coordinate (15).

This suggests a consistent decrease of 20 units in the y-coordinates.

Assuming this pattern continues, we can predict the coordinates of Item 3.

For Item 3:

x-coordinate = Item 2's x-coordinate + 13 units = 15 + 13 = 28

y-coordinate = Item 2's y-coordinate - 20 units = -5 - 20 = -25

Therefore, the predicted coordinates of Item 3 are (28, -25).