To find a possible coordinate of Mia's house, we can use the distance formula. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, the park is at the point \((4, -2)\), and Mia's house is 7 units away from the park. We can let the coordinates of Mia's house be \((x, y)\). The distance from Mia's house to the park can be expressed as:
\[ 7 = \sqrt{(4 - x)^2 + (-2 - y)^2} \]
Squaring both sides to eliminate the square root gives us:
\[ 49 = (4 - x)^2 + (-2 - y)^2 \]
Now we can expand and rearrange this equation:
\[ 49 = (4 - x)^2 + (-2 - y)^2 \] \[ 49 = (4 - x)^2 + (y + 2)^2 \]
This equation represents a circle with a center at the point \((4, -2)\) and a radius of 7.
To find a possible coordinate of Mia's house, we can choose a specific point that satisfies this equation. One straightforward point that is 7 units away from \((4, -2)\) can be found by moving 7 units directly to the right or left (or up or down) from the park's coordinates.
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Moving right: If we move right from \((4, -2)\), we get: \[ (4 + 7, -2) = (11, -2) \]
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Moving left: If we move left from \((4, -2)\), we get: \[ (4 - 7, -2) = (-3, -2) \]
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Moving up: If we move up from \((4, -2)\), we get: \[ (4, -2 + 7) = (4, 5) \]
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Moving down: If we move down from \((4, -2)\), we get: \[ (4, -2 - 7) = (4, -9) \]
All of these points \((11, -2)\), \((-3, -2)\), \((4, 5)\), and \((4, -9)\) are 7 units away from the park at \((4, -2)\).
Therefore, one possible coordinate of Mia's house is:
\((11, -2)\)