A taxicab starts at (1, -2) on the grid. It goes 3 blocks east and 1 block south to pick up a passenger. Then it goes 6 blocks west and 5 blocks north and drops off the passenger. What are the coordinates of the point where the passenger was dropped off?

https://dlap.gradpoint.com/Resz/~0.YJZ4B5XcvlgKwuFB.SNoLza7MzsPOJ2LU4NCm5lf3NSWrIepzEYv8pYPN1dU/11335527,A01,111,0,0,0,0/Assets/testitemimages/geometry_b/transformations/mc003-1.jpg

(4, 8)

(4, 2)

(-2, 2)

(-2, 8)

Question

A taxicab starts at (1, -2) on the grid. It goes 3 blocks east and 1 block south to pick up a passenger. Then it goes 6 blocks west and 5 blocks north and drops off the passenger. What are the coordinates of the point where the passenger was dropped off?

https://dlap.gradpoint.com/Resz/~0.YJZ4B5XcvlgKwuFB.SNoLza7MzsPOJ2LU4NCm5lf3NSWrIepzEYv8pYPN1dU/11335527,A01,111,0,0,0,0/Assets/testitemimages/geometry_b/transformations/mc003-1.jpg

(4, 8)

(4, 2)

(-2, 2)

(-2, 8)

Narad · Answer

The initial point is $$(1,2)$$

Going East is positive x
Going West is negative x
Going North is positive y
Going South is negative y
The displacements are
(3,-1)
(-6,5)
The final position is
$$=(1, -2)+(3,-1)+(-6,5)= (-2, 2)$$
The answer is (-2,2)