The correct answer is:
[tex]T_{(3,1)} \circ R_{O,270^{\circ}}[/tex]
Explanation:
The coordinates of RSTU are:
R(-5, -4)
S(-4, -2)
T(-1, -3)
U(-3, -5)
The coordinates of R''S''T''U'' are:
R''(-3, 2)
S''(-1, 1)
T''(-2, -2)
U''(-4, 0)
[tex]T_{(3, 1)}[/tex] is a translation 3 units right and 1 unit up. This adds 3 to the x-coordinate of each point and 1 to the y-coordinate of each point. This gives us:
R(-5, -4)→R'(-2, -3)
S(-4, -2)→S'(-1, -1)
T(-1, -3)→T'(2, -2)
U(-3, -5)→U'(0, -4)
[tex]R_{O,270^{\circ}}[/tex] is a rotation 270° clockwise about the rotation. This negates the x-coordinate and switches it and the y-coordinate. Algebraically,
(x, y)→(y, -x)
When this is applied to R'S'T'U', we have:
R'(-2, -3)→R''(-3, 2)
S'(-1, -1)→S''(-1, 1)
T'(2, -1)→T''(-1, -2)
U'(0, -4)→U''(-4, 0)
These are the correct coordinates of R''S''T''U'', so this is the correct answer.
