To find the coordinates of Point D, we know that Point D must have the same second coordinate (y-coordinate) as Point A, which is 4. Therefore, we can represent Point D as (x, 4).
Additionally, we are given that line segment AD is 3 cm in length. To calculate the distance between points A and D, we can use the distance formula in the context of the coordinate plane.
Point A is at (-9, 4), so we have:
- The y-coordinate of Point D is 4.
- The x-coordinate of Point D can be determined by the distance formula:
\[ \text{Distance} = |x_D - x_A| = |x_D - (-9)| = |x_D + 9| \] We need this distance to equal 3 cm. Therefore,
\[ |x_D + 9| = 3 \]
This equation gives us two possible scenarios:
- \(x_D + 9 = 3\) which leads to \(x_D = 3 - 9 = -6\)
- \(x_D + 9 = -3\) which leads to \(x_D = -3 - 9 = -12\)
Since Point D must be plotted on the coordinate plane, we need to ensure that the x-coordinate is within a reasonable range based on the provided information.
Clearly, the only suitable answer based on the choices given is \((-6, 4)\).
Thus, the coordinates of Point D are: \[ \text{(−6, 4)} \]