Question

Find the image of triangle vty for the given glide reflection.

Answer 1

A glide reflection is a type of symmetry that combines a translation and a reflection. The translation is in a direction perpendicular to the reflection, and the reflection is about a line that passes through the translation.

The image of a figure under a glide reflection is a mirror image of the figure, reflected across the line of reflection.

To find the image of a triangle under a glide reflection, you can first find the image of each point on the triangle. Then, you can connect the image points to form the image triangle.

For example, if you have a triangle with vertices A, B, and C, and the glide reflection is reflected across the line y = x, then the image of A would be at point (-Ax, Ay), the image of B would be at point (-Bx, By), and the image of C would be at point (-Cx, Cy).

You can then connect the image points to form the image triangle, which would be a mirror image of the original triangle, reflected across the line y = x.

Explanation:

I cannot straight up give the answer.

Answer 2

• V'(-2, -1) ⇒ V''(1, 2)
• T'(-1, -3) ⇒ T''(3, 1)
• Y'(2, 0) ⇒ Y''(0, -2)

Explanation:

You want the coordinates of the vertices of the given triangle after translation right 3 and down 3, followed by reflection over the line y=-x.

Transformations

The "glide" transformation adds (3, -3) to each coordinate pair. For example, ...

V(-5, 2) ⇒ V'(-5+3, 2 -3) = V'(2, -1)

The "reflection" transformation swaps the x- and y-coordinates, negating both. For example, ...

T'(-1, -3) ⇒ T''(3, 1)

The transformed coordinates are ...

• V'(-2, -1) ⇒ V''(1, 2)
• T'(-1, -3) ⇒ T''(3, 1)
• Y'(2, 0) ⇒ Y''(0, -2)

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Additional comment

The coordinates in the calculator output are listed [x, y] on each row of the matrix. The rows correspond to V, T, Y from top down.