Question

On graph paper, draw and label ΔABC, whose vertices have the coordinates A(1, 2), B(6, 3), and C(4, 6). b. Under the translation P(x, y) → P'(x + 5, y - 3), the image of ΔABC is ΔA'B'C'. Find the coordinates of A', B', and C'. c. On the same graph drawn in part a, draw and label ΔA'B'C'.

Answer 1

The translated coordinates of ΔA'B'C' are A'(6, -1), B'(11, 0), and C'(9, 3). The translation moves the triangle 5 units to the right and 3 units down.

Step-by-step explanation:

The student is asked to perform a geometric translation on triangle ΔABC with vertices at A(1, 2), B(6, 3), and C(4, 6). The translation rule P(x, y) → P'(x + 5, y - 3) is applied to find the coordinates of the translated triangle ΔA'B'C'.

Applying the translation to each vertex:

• A'(1 + 5, 2 - 3) = A'(6, -1)
• B'(6 + 5, 3 - 3) = B'(11, 0)
• C'(4 + 5, 6 - 3) = C'(9, 3)

To graphically represent both triangles, the original triangle ΔABC with its given coordinates is plotted on graph paper first. Subsequently, the new coordinates of the translated triangle ΔA'B'C' are plotted, resulting in a triangle that is shifted 5 units to the right and 3 units down from the original position.

Note: To properly execute this task, a ruler and graph paper are necessary for accurate representation.