Question

3 On a coordinate grid, the location of a lighthouse is at L, and the location of a buoy is at B. At noon, a ship is at the midpoint of the segment connecting the buoy and the lighthouse on the grid. Find the coordinates that best represent the ship's position at noon?​

Answer 1

`((1)/(2), 2)`

Explanation:

Using the midpoint formula,
`M((x_1 + x_2)/(2), (y_1 + y_2)/(2))`, we can find the coordinates that represents the position of the ship at noon.

Let
`L(-4, 7) = (x_1, y_1)` (given on the coordinate plane)

`B(5, -3) = (x_2, y_2)` (given also)

Plug in the values into the formula and solve as follows:

`M((-4 + 5)/(2), (7 +(-3))/(2))`

`M((1)/(2), (7 - 3)/(2))`

`M((1)/(2), (4)/(2))`

`M((1)/(2), 2)`

Position of the ship at noon is best represented at
`((1)/(2), 2)`