Segment FG begins at point F(-2, 4) and ends at point G (-2, -3). Segment FG is translated by (x, y) → (x – 3, y + 2) and then reflected across the y-axis to form segment F'G'. How long is segment F'G'?

The length of the segment F'G' is 7.

Step-by-step explanation:

From Linear Algebra we define reflection across the y-axis as follows:

, (Eq. 1)

In addition, we get this translation formula from the statement of the problem:

, (Eq. 2)

Where:

- Original point, dimensionless.

- Transformed point, dimensionless.

If we know that and , then we proceed to make all needed operations:

Translation

Reflection

Lastly, we calculate the length of the segment F'G' by Pythagorean Theorem:

The length of the segment F'G' is 7.

`1234567890-=/*-qwertyuiop[]asdfghjkl; '\\zxcvbnm,./+ /