Answer:
Step-by-step explanation:
You want the coordinates of points J(1, -2), R(-3, 6), B(4, 5) after translation by (2, 1) and reflection over y = x.
Translation adds the translation vector each point. Translation by (2, 1) is the transformation ...
(x, y) ⇒ (x +2, y +1)
Reflection over the line y = x causes the coordinates of a point to be swapped:
(x, y) ⇒ (y, x)
The composition of the two transformations, translation by (2, 1) and reflection over y=x, results in the transformation ...
(x, y) ⇒ (y +1, x +2)
That moves the given points to ...
J(1, -2) ⇒ J''(-1, 3)
R(-3, 6) ⇒ R''(7, -1)
B(4, 5) ⇒ B''(6, 6)
__
Additional comment
The attachment shows the translated ∆JRB and the same triangle after reflection over the diagonal line y = x. The final position is in red.