Question

A triangle is shown.

Drag graphs to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, or the line y=x.

Answer 1

Reflecting over the x axis means to reflect the image vertically, so the result is the second from the right.

Similarly, reflecting over the y axis means to reflect the image horizontally, so the result is the second.

Finally, reflecting over the y=x line means to reflect the image over the bisector of first and third quadrant, so the result is the fourth

Answer 2

The vertices of triangle after reflation across x-axis are (1,3), (3,2), (4,5).

The vertices of triangle after reflation across y-axis are (-1,-3), (-3,-2), (-4,-5).

The vertices of triangle after reflation across y=x are (-3,1), (-2,3), (-5,4).

Explanation:

From the given figure it is clear that the vertices of triangle are (1,-3), (3,-2), (4,-5).

If a figure reflected over the x-axis, then

`(x,y)\rightarrow (x,-y)`

`(1,-3)\rightarrow (1,3)`

`(3,-2)\rightarrow (3,2)`

`(4,-5)\rightarrow (4,5)`

The vertices of triangle after reflation across x-axis are (1,3), (3,2), (4,5).

If a figure reflected over the y-axis, then

`(x,y)\rightarrow (-x,y)`

`(1,-3)\rightarrow (-1,-3)`

`(3,-2)\rightarrow (-3,-2)`

`(4,-5)\rightarrow (-4,-5)`

The vertices of triangle after reflation across y-axis are (-1,-3), (-3,-2), (-4,-5).

If a figure reflected over the y=x, then

`(x,y)\rightarrow (y,x)`

`(1,-3)\rightarrow (-3,1)`

`(3,-2)\rightarrow (-2,3)`

`(4,-5)\rightarrow (-5,4)`

The vertices of triangle after reflation across y=x are (-3,1), (-2,3), (-5,4).