To find the coordinates of Point D such that it has the same second coordinate as Point A and lies 3 cm away from Point A, we start with the coordinates of Point A, which are \((-9, 4)\).
Since Point D must have the same y-coordinate as Point A, its y-coordinate should also be \(4\). We can represent Point D as \((x, 4)\).
Now, we need to find an x-coordinate for Point D such that the distance between Point A \((-9, 4)\) and Point D \((x, 4)\) is \(3\) cm.
The distance formula in this case is simplified because the y-coordinates are the same:
\[ \text{Distance} = |x_2 - x_1| = |x - (-9)| = |x + 9| \]
We want this distance to be equal to 3:
\[ |x + 9| = 3 \]
This absolute value equation gives us two scenarios:
-
\(x + 9 = 3\)
- Solving this gives: \[ x = 3 - 9 = -6 \]
-
\(x + 9 = -3\)
- Solving this gives: \[ x = -3 - 9 = -12 \]
Thus, the possible coordinates for Point D are:
- At \((-6, 4)\) (which is valid as it lies within the bounds on the coordinate plane)
- At \((-12, 4)\) (which is outside the range of x-values on the provided coordinate plane)
Now, looking at the answer choices provided:
- (4, −6)
- (6, −4)
- (−2, 4)
- (−6, 4)
The only valid coordinate for Point D that meets the criteria of having the same y-coordinate as Point A and being 3 cm away is \((-6, 4)\).
Thus, the answer is:
\[ \text{Point D coordinates: } (-6, 4) \]