Question

A movie theater is 4 kilometers east and 2 kilometers south of your house.

Answer 1

A) (4,-2) is the theater
B) (-1,1) is the restaurant

Answer 2

a. (+4, -2)

We can use the following conventions:

- x-axis: east-west direction, with east being positive x and west being negative x

- y-axis: north-south direction, with north being positive y and south being negative y

With this coordinates, the movie theater is:

- 4 km east --> this means x = +4

- 2 km south --> this means y = -2

So, the coordinates of the theater are (+4,-2)

b. (-1,+1)

We drive 5 km west (which means $\Delta x = -5$) and 3 km north (which means $\Delta y = +3$). We have to add these displacements to each coordinate. we find:

$x'= x_0 + \Delta x = +4 + (-5) = -1\\y' = y_0 + \Delta y = -2 + (+3)=+1$

So, the coordinates of the restaurant are (-1, +1)