A'B'C' based on the triangle ABC and the translation vector shown, we need to apply the translation vector to each of the points in the triangle ABC.
The translation vector is a displacement that specifies the distance and direction that each point in the triangle should be moved. In this case, the translation vector is (2, 3), which means that each point should be moved 2 units to the right and 3 units up.
We can apply the translation vector to each point in the triangle by adding the x- and y-coordinates of the vector to the x- and y-coordinates of each point.
For example, to find the coordinates of A' based on the coordinates of A and the translation vector, we would do the following:
A'x = Ax + translation vector x
= -1 + 2
= 1
A'y = Ay + translation vector y
= -1 + 3
= 2
Therefore, the coordinates of A' are (1, 2).
We can use the same process to find the coordinates of B' and C':
B'x = Bx + translation vector x
= 3 + 2
= 5
B'y = By + translation vector y
= 2 + 3
= 5
Therefore, the coordinates of B' are (5, 5).
C'x = Cx + translation vector x
= 4 + 2
= 6
C'y = Cy + translation vector y
= 0 + 3
= 3
Therefore, the coordinates of C' are (6, 3).
Therefore, the correct points for A'B'C' based on the triangle ABC and the translation vector shown are:
A' (1, 2) B'(5, 5) C'(6, 3)
The other options listed do not satisfy the conditions given in the problem ♂️