Point D is located at the coordinates (-2, -2). To find points E and F, which are each 88 units away from point D, we can use the formula for the distance between two points in a coordinate plane. The points E and F will lie on a circle with a radius of 88 units centered at point D.
The distance formula is given by:
\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = r \]
where \((x_1, y_1)\) are the coordinates of point D, \((x_2, y_2)\) are the coordinates of points E and F, and \(r\) is the radius (88 units).
Using point D \((-2, -2)\), the equation for the circle becomes:
\[ \sqrt{(x + 2)^2 + (y + 2)^2} = 88 \]
Squaring both sides, we get:
\[ (x + 2)^2 + (y + 2)^2 = 88^2 \]
Calculating \(88^2\):
\[ 88^2 = 7744 \]
So, the equation of the circle is:
\[ (x + 2)^2 + (y + 2)^2 = 7744 \]
To find specific points E and F, we can choose specific angles or directions from point D. For simplicity, let's find two points along the horizontal and vertical directions.
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Point E (Horizontal direction):
- If we move 88 units to the right of point D, we can calculate the coordinates of point E as follows: \[ E = (-2 + 88, -2) = (86, -2) \]
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Point F (Vertical direction):
- If we move 88 units upward from point D, we calculate the coordinates of point F: \[ F = (-2, -2 + 88) = (-2, 86) \]
Thus, the coordinates of points E and F, located 88 units away from point D, are:
E = (86, -2) and F = (-2, 86).
Points E and F can exist in multiple locations based on the circle we've established, but according to the choices made in movement direction, we have two specific coordinates. There are infinitely many solutions for points E and F that satisfy the distance condition, as they can be located anywhere around the circle.