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

Answer:

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

Step-by-step 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).