Question

describe specifically the formal transformation that occured when the original points were moved 4 points left and 2 points down

Answer 1

When you move a point in a two-dimensional Cartesian coordinate system, you're performing a transformation represented mathematically. To describe the formal transformation that occurs when the original points are moved 4 units to the left and 2 units down, let's establish some key components.

Assume the original point in the coordinate system is given by \((x, y)\).

### Transformation Process:

1. **Moving 4 Units to the Left**: This transformation affects the x-coordinate of the point. To move a point left by 4 units, you subtract 4 from the x-coordinate:
\[
x' = x - 4
\]

2. **Moving 2 Units Down**: This transformation affects the y-coordinate of the point. To move a point down by 2 units, you subtract 2 from the y-coordinate:
\[
y' = y - 2
\]

### Resulting Point:

After applying both transformations, the new coordinates \((x', y')\) of the point can be represented as:
\[
(x', y') = (x - 4, y - 2)
\]

### Putting It All Together:

In summary, the formal transformation can be represented as:
\[
T: (x, y) \mapsto (x - 4, y - 2)
\]

This means every point \((x, y)\) in the original set is transformed to a new point \((x - 4, y - 2)\) after the specified translation.