Question

Triangle RST has the vertices R(2, 3), S(-2, 1), and T(-1, 5). What are the coordinates after the two transformations: Reflection over the y-axis and rotation at 180 degrees around the origin

Answer 1

R''(2,-3), S''(-2,-1) and T'(-1,-5).

Explanation:

The given vertices of triangle are R(2, 3), S(-2, 1), and T(-1, 5).

Reflection over the y-axis:

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

Using this rule, the vertices after reflection are

`R(2,3)\to R'(-2,3)`

`S(-2,1)\to S'(2,1)`

`T(-1,5)\to T'(1,5)`

Rotation at 180 degrees around the origin.

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

Using this rule, the vertices after reflection are

`R'(-2,3)\to R''(2,-3)`

`S'(2,1)\to S''(-2,-1)`

`T'(1,5)\to T''(-1,-5)`

Therefore, the coordinates of vertices after the two transformations are R''(2,-3), S''(-2,-1) and T'(-1,-5).