A triangle has vertices of Q(2,¨C3), R(4, ¨C4), and S(5, ¨C1). Give the coordinates of its image after a glide reflection containing a translation of (x, y) ¡ú (x, y + 5) and a reflection in the y-axis
To find the image of the triangle after a glide reflection, we need to apply both the translation and the reflection operations to each vertex of the original triangle.
Let's start with the translation operation: (x, y) -> (x, y + 5)
For vertex Q(2, -3), applying the translation yields Q'(2, -3 + 5) = Q'(2, 2).
For vertex R(4, -4), applying the translation yields R'(4, -4 + 5) = R'(4, 1).
For vertex S(5, -1), applying the translation yields S'(5, -1 + 5) = S'(5, 4).
Now let's move on to the reflection in the y-axis. This operation simply involves changing the sign of the x-coordinate of each vertex.
For Q', the reflection in the y-axis gives us Q"(-2, 2).
For R', the reflection in the y-axis gives us R'(-4, 1).
For S', the reflection in the y-axis gives us S'(-5, 4).
Therefore, the coordinates of the image triangle after the glide reflection are Q"(-2, 2), R'(-4, 1), and S'(-5, 4).