Question

Sketch triangle PQR, where P = (1,1), Q = (1,2), and R = (3,1). For each of the following, apply the given transformation T to the vertices of triangle PQR, sketch the image triangle P′Q′R′, then decide which of the terms reflection, rotation, translation, or glide-reflection accurately describes the action of T . Provide appropriate detail to justify your choices.
(a) T (x, y) = (x + 3, y − 2)
(b) T (x, y) = (y, x)
(c) T (x, y) = (−x + 2, −y + 4)
(d) T (x, y) = (x + 3, −y)

Answer 1

@jim_thompson5910

Answer 2

Show me what you have so far

Answer 3

Well I thought that (y, x) would be a rotation because point P's image would be (1, 1). Since the new figure also shares that point it can be a rotation.

Answer 4

(x,y) ---> (y,x) is a reflection over the line y = x

Answer 5

When I graph it I don't see it

Answer 6

try a few points like (2,3) and (5,7)

Answer 7

Yeah i guess i see it

Answer 8

And then (x+3, y-2) is a translation

Answer 9

(-x + 2, -y + 4) is a rotation

Answer 10

`(x+3, y-2) is a translation `
yes

Answer 11

(x + 3, y) is a glide-reflection

Answer 12

`(x + 3, y) is a glide-reflection `
half true
there is a glide, but not a reflection

it's simply a translation

Answer 13

`(-x + 2, -y + 4) is a rotation `
this is the glide reflection

Answer 14

why?

Answer 15

wait it reflects across x = 1 and then translates y + 2

Answer 16

so it's a glide-reflection

Answer 17

well going from x to -x is the reflection part
then adding on 2 is the translation part

Answer 18

thanks! i just have two more questions left. i am really appreciating ur help (as always)