The points are C. (-9, -2), (-5, 3), and (0, -3).
Step-by-step explanation:
Step 1:
The triangle undergoes a translation and then a rotation.
The translation is that the units are translated 5 units to the right.
So the rule for the translation is (x+5, y).
The coordinate (4, 2) becomes (9, 2).
The coordinate (0, -3) becomes (5, -3).
The coordinate (-5, 3) becomes (0, 3).
Step 2:
When the points are rotated the x and y values are not interchanged and the symbol depends on the quadrant in which the shape is reflected on to.
The points (9, 2) and (0, 3) are in the first quadrant. After translation, they will be in the third quadrant where the x and y values are both negative.
The point (5, -3) is in the fourth quadrant. After translation, it will be in the second quadrant where the x value is negative and the y value is positive.
The coordinate (9, 2) becomes (-9, -2).
The coordinate (0, 3) becomes (0, -3).
The coordinate (5, -3) becomes (-5, 3).
So the points are (-9, -2), (-5, 3), and (0, -3) which is option C.
