Question

A line contains the points left parenthesis, negative 4 , 2 , right parenthesis−4, 2and left parenthesis, negative 4 , 6 , right parenthesis .−4, 6.The line is translated 2 units down and 3 to the right. What are the new points on the translated line?

Answer 1

To find the new points after translating the original points \( (-4, 2) \) and \( (-4, 6) \) 2 units down and 3 units to the right, we need to apply the translation separately to each point.

1. **Translate 2 units down:** This means we subtract 2 from the y-coordinate.
2. **Translate 3 units to the right:** This means we add 3 to the x-coordinate.

Let's apply these translations to the points one by one:

**For the point \( (-4, 2) \):**
- New x-coordinate: \( -4 + 3 = -1 \)
- New y-coordinate: \( 2 - 2 = 0 \)

So the new coordinates for the point \( (-4, 2) \) are \( (-1, 0) \).

**For the point \( (-4, 6) \):**
- New x-coordinate: \( -4 + 3 = -1 \)
- New y-coordinate: \( 6 - 2 = 4 \)

So the new coordinates for the point \( (-4, 6) \) are \( (-1, 4) \).

Thus, after the translation, the new points on the translated line are:
- \( (-1, 0) \)
- \( (-1, 4) \)