Question

Kristine made a map of the county in which she lives. She drew a coordinate plane and plotted the locations of three small towns. When the town of Lisby is added to Kristine's map, its location is the same distance from Overley as Jessup is from Kingsville. Which ordered pair could be the coordinates of Lisby?

1) (1, -3)
2) (2, -3)
3) (1, -2)

Answer 1

The ordered pair that could be the coordinates of Lisby is 2) (2, -3).

Step-by-step explanation:

To determine the possible coordinates of Lisby, we need to find a point that is equidistant from the given pairs of towns (Overley and Jessup, Kingsville). Let's consider the points:

- Overley: (0, 0)

- Jessup: (1, 0)

- Kingsville: (0, -1)

The midpoint between Overley and Jessup is ((0 + 1)/2, (0 + 0)/2) = (0.5, 0), and the midpoint between Jessup and Kingsville is ((1 + 0)/2, (0 + (-1))/2) = (0.5, -0.5). Both midpoints have the same x-coordinate of 0.5, indicating that the distance from Overley to Jessup is the same as the distance from Jessup to Kingsville.

Now, we need to find a point equidistant from Overley and Jessup. The y-coordinate of Lisby should be the same as the y-coordinate of the midpoint between Overley and Jessup, which is 0.

Therefore, Lisby's coordinates can be written as (x, 0). Looking at the provided options, (2, -3) is the only pair with a y-coordinate of 0, making it the possible coordinates of Lisby.

In summary, the ordered pair 2) (2, -3) could be the coordinates of Lisby, as it is equidistant from Overley and Jessup, similar to the relationship between Jessup and Kingsville.