To determine the possible locations of the student after walking 3 miles from the starting point [tex]\((-7, -9)\)[/tex] in one of the four cardinal directions (north, south, east, or west), let’s analyze each direction:
1. North (increasing the y-coordinate by 3):
[tex]\[ (-7, -9 + 3) = (-7, -6) \][/tex]
2. South (decreasing the y-coordinate by 3):
[tex]\[ (-7, -9 - 3) = (-7, -12) \][/tex]
3. East (increasing the x-coordinate by 3):
[tex]\[ (-7 + 3, -9) = (-4, -9) \][/tex]
4. West (decreasing the x-coordinate by 3):
[tex]\[ (-7 - 3, -9) = (-10, -9) \][/tex]
Thus, the possible locations for the student after walking 3 miles from the starting point [tex]\((-7, -9)\)[/tex] are:
[tex]\[
(-10, -9), (-4, -9), (-7, -6), (-7, -12)
\][/tex]
Now, let's identify these possible locations in the provided multiple-choice options:
1. Option 1:
[tex]\[ (-10, -9), (-4, -9), (-7, -6), (-7, -12) \][/tex]
These are valid locations as per our calculations.
2. Option 2:
[tex]\[ (-9, -7), (-12, -7), (-4, -6), (-10, -6) \][/tex]
None of these points match our calculated points.
3. Option 3:
[tex]\[ (-7, 3), (-7, -12), (-4, -9), (3, -9) \][/tex]
The points [tex]\((-7, -12)\)[/tex] and [tex]\((-4, -9)\)[/tex] are valid, but the others are not calculated.
4. Option 4:
[tex]\[ (3, -9), (6, -9), (-7, -4), (-7, -12) \][/tex]
Only [tex]\((-7, -12)\)[/tex] is valid here.
The correct set of points corresponds to Option 1:
[tex]\[ (-10, -9), (-4, -9), (-7, -6), (-7, -12) \][/tex]
So, the possible locations for the student after walking 3 miles in one of the cardinal directions are:
[tex]\[ (-10, -9), (-4, -9), (-7, -6), (-7, -12) \][/tex]
