To find the locations of points Y and Z, which are each 6 units away from Point X located at (-20, -20), we can use the concept of distance in a Cartesian coordinate system.
Point X's coordinates are \((-20, -20)\). The distance formula tells us 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 want \(d = 6\) units, so we can set up the equation around the point X \((-20, -20)\):
Let point Y be at \((x, y)\). Then, we have:
\[ \sqrt{(x - (-20))^2 + (y - (-20))^2} = 6 \]
This simplifies to:
\[ \sqrt{(x + 20)^2 + (y + 20)^2} = 6 \]
Squaring both sides, we get:
\[ (x + 20)^2 + (y + 20)^2 = 36 \]
This equation describes a circle with a radius of 6 centered at point X (-20, -20).
To find the specific coordinates of points Y and Z, we can explore possible directions. Since we are looking for two locations 6 units away, we can use known angles or directions.
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Point Y: If we move directly to the right (east) from point X (-20, -20):
- Coordinates will be:
- \((-20 + 6, -20)\) = (-14, -20)
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Point Z: If we move directly upwards (north) from point X:
- Coordinates will be:
- \((-20, -20 + 6)\) = (-20, -14)
Thus, two possible locations for points Y and Z are:
- Y = (-14, -20)
- Z = (-20, -14)
There are infinitely many possible points, but these are two specific examples that satisfy the requirement. To find additional points, you can use angles like 45 degrees or any other direction specified.
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