Final answer:
After translating the triangle defined by A(1,5), B(2,3), and C(-4,3) 5 units to the right, the new coordinates are A'(6,5), B'(7,3), and C'(1,3).
Step-by-step explanation:
The student is asking about the translation of a triangle in a coordinate plane. The triangle is defined by the points A(1,5), B(2,3), and C(-4,3) initially. Translating a shape on the coordinate plane involves shifting every point of the shape by the same amount. In this case, the triangle is being translated 5 units to the right. Translation to the right means we add 5 to the x-coordinate of each point of the triangle.
A' would be (1+5,5) or (6,5), B' would be (2+5,3) or (7,3), and C' would be (-4+5,3) or (1,3). Therefore, the coordinates of the resulting triangle ABC after the translation are A'(6,5), B'(7,3), and C'(1,3).