Point F is located at the coordinates \((-17, -17)\). Since Points G and H are each 5 units away from Point F, we can determine their locations using the distance formula.
To find points that are 5 units away from F, we can use the concept of a circle with a radius of 5 centered at F. The equation of the circle would be:
\[ (x + 17)^2 + (y + 17)^2 = 5^2 \]
This simplifies to:
\[ (x + 17)^2 + (y + 17)^2 = 25 \]
To find specific points, we can look for coordinates that satisfy this equation.
One straightforward approach is to calculate a few specific points. We can add and subtract 5 to/from the x or y coordinate of point F:
-
Moving right 5 units:
- G could be at: \((-17 + 5, -17) = (-12, -17)\)
-
Moving left 5 units:
- H could be at: \((-17 - 5, -17) = (-22, -17)\)
-
Moving up 5 units:
- G could also be at: \((-17, -17 + 5) = (-17, -12)\)
-
Moving down 5 units:
- H could also be at: \((-17, -17 - 5) = (-17, -22)\)
Thus, some possible coordinates for points G and H that are each 5 units away from point F can be:
- \(G(-12, -17)\)
- \(H(-22, -17)\)
or
- \(G(-17, -12)\)
- \(H(-17, -22)\)
In summary, there are many combinations for points G and H, but they are all located 5 units from point F, \((-17, -17)\).
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