Question

Triangle ABC has coordinates A(-1, 3), B(2, 2), and C(3, -6). If the triangle is translated 3 units to the left, find the coordinates of A'.

Answer 1

To translate point A(-1, 3) 3 units to the left, subtract 3 from the x-coordinate, giving us A' (-4, 3), as the y-coordinate does not change.

Step-by-step explanation:

The student's question is about performing a translation of a triangle on the Cartesian coordinate system. A translation is a type of geometric transformation that slides each point of a figure the same distance in the same direction. In this case, point A of triangle ABC will be translated 3 units to the left.

To translate a point to the left, we simply subtract the translation amount from the x-coordinate of the point. Therefore, to find the coordinates of A', we take the x-coordinate of A, which is -1, and subtract 3 from it, resulting in an x-coordinate of -4 for A'. The y-coordinate remains unchanged, so the y-coordinate for A' is 3. Thus, the coordinates for A' after being translated 3 units to the left are (-4, 3).