Answer: The co-ordinates of the vertices of triangle A'B'C' are A(-3, 3), B'(-1, 1) and C'(-2, 3).
Step-by-step explanation: Given that the triangle ABC is reflected across the x-axis and then translated 4 units up to create triangle A'B'C'.
We are to find the co-ordinates of the vertices of triangle A'B'C'.
From the figure, we note that
the co-ordinates of the vertices of triangle ABC are A(-3, 1), B(-1, 3) and C(-2, 1).
The reflection across X-axis changes the co-ordinates of a point according to the following rule :
(x, y) ⇒ (x, -y).
So, after reflecting across X-axis, the co-ordinates of the vertices of triangle ABC will become :
A(-3, 1) ⇒ (-3, -1),
B(-1, 3) ⇒ (-1, -3),
C(-2, 1) ⇒ (-2, -1).
Now, translating a point 4 units up will change the co-ordinates as follows :
(x, y) ⇒ (x, y+4).
Therefore, after translating the reflected triangle 4 units up, the fianl co-ordinates of triangle a'B'C' will become
(-3, -1) ⇒ (-3, -1+4) = (-3, 3),
(-1, -3) ⇒ (-1, -3+4) = (-1, 1),
(-2, -1) ⇒ (-2, -1+4) = (-2, 3).
Thus, the co-ordinates of the vertices of triangle A'B'C' are A(-3, 3), B'(-1, 1) and C'(-2, 3).
