17. the vertices of triangle abc are a(-1, 1), b(0, 3), and c(3, 4). graph the i

Question

17. the vertices of triangle abc are a(-1, 1), b(0, 3), and c(3, 4). graph the image of triangle abc after a composition of the following transformatios in the order they are listed.
- translation: (x, y) -> (x -3, y- 3)
- reflection: in the line y=x
- yes or no: is the composition a glide reflection?
- yes or no: is the image the same if the ordee of the transformations is switched? (reflection, then glide)

18. the vertices of triangle abc are a(-1, 1), b(0, 3), and c(3, 4) graph the image of triangle abc after a composition of the following transformations in the order they are listed.
- rotation: 90 degrees counterclockwise above the origin
- reflection: in the y- axis
- yes or no: if the transformations were performed in reverse order (reflection, then rotation), would the final image ne the same?
- yes or no: would the reflection of triangle abc in the line y = x have produced the same final image?

Explanation / Answer

17. Given vertices are: (-1,1), (0,3) and (3,4)

After translation, the points become: (-1-3,1-3),(0-3,3-3),(3-3,4-3) that is (-4,-2),(-3,0) and (0,1)

So reflecting over x=y, the points (h,k) becomes (k,h)

So we would get:(-2,-4),(0,-3) and (1,0)

When we see the points, we see that this is a glide reflection

So of the points are reflected first and then translated, we get:

(-1,1),(0,3),(3,4)-->(1,-1),(3,0),(4,3)----->(1-3,-1-3),(3-3,0-3),(4-3,3-3)--->(-2,-4),(0,-3),(1,0)

So the image would be the same even when the order is changed.

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18. Given vertices are: (-1,1), (0,3) and (3,4)

When rotated 90 degrees in counterclockwise, the point (h,k) becomes (-k,h)

So we get the points as: (-1,-1)(-3,0)(-4,3)

When reflected in the y axis, the point (h,k) becomes (-h,k)

So we get the points as (1,-1),(3,0)(4,3)

So if the transformation is performed in reverse order, we get:

(-1,1), (0,3), (3,4)--->(1,1)(0,3),(-3,4)--->(-1,1),(-3,0),(-4,-3)

So when performed in the reverse order, the transformation is not the same

Reflection of the point (h,k) over the line x=y is given by (k,h)

So reflection of the given points would be (1,-1)(3,0)(4,3)

So the final image would be same if relected over the line x=y

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