To find the coordinates of Point F such that the line segment FD has a length of 2 cm and both points share the same second coordinate, we start with the coordinates of Point D, which is at (-3, 1). Since Point F must have the same y-coordinate as Point D, its coordinates will be in the form of (-x, 1).
Given that we want the distance between Point D and Point F (FD) to be 2 cm, we can set up the distance formula. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In our case, the points are D (-3, 1) and F (x, 1). Thus, we only need to consider the x-coordinates:
\[ d = \sqrt{(x - (-3))^2 + (1 - 1)^2} = \sqrt{(x + 3)^2} \]
Now, we set the distance equal to 2:
\[ \sqrt{(x + 3)^2} = 2 \]
This leads us to two equations:
- \(x + 3 = 2\)
- \(x + 3 = -2\)
Solving the first equation:
\[ x + 3 = 2 \implies x = 2 - 3 = -1 \]
Solving the second equation:
\[ x + 3 = -2 \implies x = -2 - 3 = -5 \]
However, Point F must be within the bounds of the same coordinate plane indicated in the question, so we have the possible coordinates for Point F:
- (-1, 1)
- (-5, 1) (not a valid choice since it falls outside the x bounds given in the coordinate plane).
Thus, the only valid option for Point F, which maintains the same y-coordinate as Point D and results in a line segment FD of length 2 cm, is:
\((-1, 1)\)
So the answer is: \[ \text{(−1, 1)} \]