Question

The vertices of Δabc are a(2, -3), b(-3, -5), and c(4, 1). For each translation, give the vertices of Δa′b′c′.

Answer 1

To find the vertices of the translated triangle ΔA'B'C', simply add each component of the translation vector to the corresponding components of each vertex of ΔABC. For example, if the translation vector is (3, 2), then the new vertices would be A'(5, -1), B'(0, -3), and C'(7, 3).

Step-by-step explanation:

The vertices of ΔABC are A(2, -3), B(-3, -5), and C(4, 1). To find the vertices of the translated ΔA'B'C' for a given translation, you need to add the translation vector to each of the vertices of ΔABC. If the translation vector is (x, y), then the coordinates of the new vertices would be A'(2+x, -3+y), B'(-3+x, -5+y), and C'(4+x, 1+y).

For example, if the translation vector is (3, 2), then:

• Vertex A' would be (2+3, -3+2) = (5, -1)
• Vertex B' would be (-3+3, -5+2) = (0, -3)
• Vertex C' would be (4+3, 1+2) = (7, 3)

To find the new vertices for any other translation, simply apply the same process using the specific translation vector given.