P P'(–4, –7) for the glide reflection where the translation is (x, y) (x,y-4) and the line of reflection is x= -1. Find the coordinates of P
A.(-4,-11)
B.(2,-7)
C.(2,-3)
D.(-4,-3)
To solve this problem, we will follow these steps:
1. Start with point P'(–4, –7).
2. Apply the translation transformation, which is (x, y) → (x, y - 4). Since P' has coordinates (–4, –7), we can apply this transformation as follows:
P:(x, y) → (–4, –7 - 4)
→ (–4, –11)
3. Next, consider the line of reflection, which is x = -1. Reflect point P about this line.
- The line x = -1 is a vertical line passing through x = -1. To reflect a point across this line, we need to find the point that is equidistant from the line but on the opposite side.
- Since P:(–4, –11) is to the left of the line x = -1, the reflected point will be to the right of the line.
- To find the reflected x-coordinate, we add the distance from P to the line (which is 3 units) to the x-coordinate of the line:
reflected x-coordinate = x-coordinate of the line + distance from P to the line
= -1 + 3
= 2
- The y-coordinate remains the same since it is equidistant from the line.
4. The coordinates of point P after the glide reflection are (2, -11).
Therefore, the correct answer is option B: (2,-7).