Find the glide reflection image of the dashed triangle where the translation is (x,y) → (x,y-3) and line of reflection is x = 2(1 point)
To find the glide reflection image of the dashed triangle with the given translation and line of reflection, we need to first perform the translation and then reflect the translated triangle across the line of reflection.
1. Translate the dashed triangle by (x,y) → (x,y-3):
Let's denote the vertices of the dashed triangle as A', B', and C', after the translation we have:
A'(x, y-3)
B'(x+4, y-3)
C'(x+2, y-6)
2. Reflect the translated triangle across the line x = 2:
Since the line of reflection is x = 2, we need to reflect the points of the translated triangle across this line. To reflect a point (x, y) across the line x = 2, we replace x by 4 - x:
Reflecting A': A''(4-x, y-3)
Reflecting B': B''(4-(x+4), y-3) = (0-x, y-3)
Reflecting C': C''(4-(x+2), y-6) = (2-x, y-6)
The glide reflection image of the dashed triangle with the given translation and line of reflection is the triangle formed by connecting the points A'', B'', C''. So, the triangle formed by A'', B'', and C'' is formed by:
A''(4-x, y-3)
B''(0-x, y-3) = (-x, y-3)
C''(2-x, y-6)
Therefore, the glide reflection image of the dashed triangle is the triangle with vertices at (4-x, y-3), (-x, y-3), and (2-x, y-6).