Question

What set of reflections would carry triangle ABC onto itself? triangle ABC on the coordinate plane with point A at 1, 2, point B at 2, 4, and point C at 3, 0.

Answer 1

y-axis, x-axis , y-axis and x-axis

Explanation:

Given : In triangle ABC

The coordinates are

A = (1,2) , B=(2,4) and C =(3,0)

Rule of reflection:

*Reflecting a point (x, y) across the y-axis will map it to (-x, y).

*Reflecting a point (x, y) across the x-axis will map it to (x, -y).

If you do a reflection on coordinate point A = (1,2) across y-axis we get
`(-1 ,2)`

then, reflecting a point (-1 , 2) across x -axis we get, (-1, -2)

then, reflecting a point (-1 , -2) across y-axis we get, (1 , -2)

and

reflecting a point (1, -2) across x- axis we get the result same i.e, A =(1,2)

Similarly,

For B = (2,4) across y-axis
`\rightarrow` (-2, 4) across x- axis
`\rightarrow` (-2, -4) across y -axis
`\rightarrow` (2 , -4) across x axis
`\rightarrow` ( 2, 4) = B

for C = (3, 0) across y-axis
`\rightarrow` (-3, 0) across x- axis
`\rightarrow` (-3, 0) across y -axis
`\rightarrow` (3 , 0) across x axis
`\rightarrow` (3, 0) = C

Therefore, the set of reflection would carry triangle ABC onto itself is:

y-axis, x-axis , y-axis and x-axis

Answer 2

Your answer is Y-axis, X-axis, Y-axis, X-axis.
The A y-axis , B y-axis and C would also be reflected over the Y-axis. When you think about the coordinates on a graph, and with that also being said there all positive.