Point E is located at \((-14, -14)\). To find points F and G that are each 6 units away from point E, we can use the distance formula, which states that the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
We need to find points F and G such that the distance from E to both points is 6. Thus, we are looking for points \((x, y)\) that satisfy:
\[ \sqrt{(x + 14)^2 + (y + 14)^2} = 6 \]
Squaring both sides, we get:
\[ (x + 14)^2 + (y + 14)^2 = 36 \]
This equation represents a circle centered at point E \((-14, -14)\) with a radius of 6.
To find the coordinates of points F and G, we can move 6 units in different directions from point E. A simple way to do this is to use the angles corresponding to the cardinal directions or also to consider the four quadrants.
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Moving directly to the right (east): \[ F_1 = (-14 + 6, -14) = (-8, -14) \]
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Moving directly to the left (west): \[ F_2 = (-14 - 6, -14) = (-20, -14) \]
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Moving up (north): \[ G_1 = (-14, -14 + 6) = (-14, -8) \]
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Moving down (south): \[ G_2 = (-14, -14 - 6) = (-14, -20) \]
Thus, the points F and G can be any combination of the points found. Thus one possible choice for F could be \((-8, -14)\) and for G could be \((-14, -8)\).
In conclusion, points F and G can be:
- \((-8, -14)\)
- \((-20, -14)\)
- \((-14, -8)\)
- \((-14, -20)\)
These points represent the options for F and G that are each 6 units away from point E.
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