To solve this problem, let's break it down into a step-by-step process, following the movements of the taxicab.
1. Starting position:
The taxicab begins at coordinates [tex]\((1, -2)\)[/tex].
2. Movement to pick up the passenger:
- The taxicab moves 3 blocks east. To move east, we add 3 to the x-coordinate.
[tex]\[
x_{\text{new}} = 1 + 3 = 4
\][/tex]
- The taxicab moves 1 block south. To move south, we subtract 1 from the y-coordinate.
[tex]\[
y_{\text{new}} = -2 - 1 = -3
\][/tex]
- So, the coordinates at the passenger pick up point are [tex]\((4, -3)\)[/tex].
3. Movement to drop off the passenger:
- The taxicab moves 6 blocks west. To move west, we subtract 6 from the x-coordinate.
[tex]\[
x_{\text{new}} = 4 - 6 = -2
\][/tex]
- The taxicab moves 5 blocks north. To move north, we add 5 to the y-coordinate.
[tex]\[
y_{\text{new}} = -3 + 5 = 2
\][/tex]
- So, the coordinates at the passenger drop off point are [tex]\((-2, 2)\)[/tex].
Thus, after following these movements, the coordinates of the point where the passenger was dropped off are [tex]\((-2, 2)\)[/tex].
