Step-by-step explanation:
First, we need to identify the coordinates of the vertex of the triangle. So, the coordinates are:
A(-1, 1)
B(-4, 1)
C(-1, 4)
Then, if we reflect over the x-axis, every vertex is transformed using the following rule:
(x, y) ------> (x, -y)
So, the coordinates of the vertex are now:
A(-1, 1) -----> (-1, -1)
B(-4, 1) -----> (-4, -1)
C(-1, 4) ------> (-1, -4)
Then, we need to translate the triangle using the rule:
(x, y) --------> (x + 6, y + 2)
So, the coordinate of the translated triangle are:
(-1, -1) ---------> (-1 + 6, -1 + 2) = A'(5, 1)
(-4, -1) ---------> (-4 + 6, -1 + 2) = B'(2, 1)
(-1, -4) ---------> (-1 +6, -4 + 2) = C'(5, -2)
Therefore, the graph of the triangle after the reflection and the translation is: