Question

Triangle abc has vertices a(−3, 1), b(−3, 4), and c(−7, 1. if ∆abc is translated according to the rule (x, y) → (x − 4, y 3) to form ∆a′b′c′, how is the translation described with words?

Answer 1

The translation described by the rule (x, y) → (x − 4, y + 3) moves each point of triangle ABC 4 units left and 3 units up to form triangle A'B'C'.

Step-by-step explanation:

The student's question asks about a translation of a triangle in the Cartesian plane. Specifically, triangle ABC with vertices A(-3, 1), B(-3, 4), and C(-7, 1) is translated according to the rule (x, y) → (x − 4, y + 3). Describing this translation with words, each point of the triangle is moved 4 units to the left and 3 units up. This movement can be visualized as shifting the entire shape of the triangle without rotating or changing its size.

To illustrate:

• Point A will move from (-3, 1) to (-7, 4).
• Point B will move from (-3, 4) to (-7, 7).
• Point C will move from (-7, 1) to (-11, 4).

The transformation keeps the shape and size of triangle ABC intact, with the resulting coordinates defining the new triangle A'B'C'.