Question

There is a gas station exactly halfway between Stan and Drew's houses. The map coordinates for Stan's house are 5 miles eastand 2 miles north. The map coordinates for Drew's house are 3 miles east and 4 miles north,Find the map coordinates for the gas station. (East, North)(4.3)(3.4)(1-1)(-1.1)

Answer 1

As per the map coordinates, Stan's house is 5 miles east and 2 miles north.

We will represent the distance to the east by x and the distance to the north by y.

So, the coordinates of Stan's house, (x1, y1)=(5, 2).

As per the map coordinates, Drew's house is 3 miles east and 4 miles north.

So, the coordinates of Drew's house, (x2, y2)=(3, 4).

Let x3 and y3 be the coordinates of the gas station.

Since the gas station is exactly halfway between Stan and Drew's houses, we will use the midpoint formula to find the map coordinates for the gas station.

The midpoint formula to find the map coordinates for the gas station is given by,

`(x3,\text{ y3)=(}(x1+x2)/(2),\text{ }(y1+y2)/(2))`

Substituting the values,

`\begin{gathered} (x3,\text{ y3)=(}(5+3)/(2),\text{ }(2+4)/(2)) \\ =((8)/(2),\text{ }(6)/(2)) \\ =(4,\text{ 3)} \end{gathered}`

Therefore, the map coordinates for the gas station is (4, 3).