Question

A line contains the points `\left(-4,\ 2\right)`and `\left(-4,\ 6\right).`The line is translated 2 units down and 3 to the right. What are the new points on the translated line?

Answer 1

To translate a line, you need to adjust the coordinates of its points according to the translation rule. Here, we have two translations:

1. **Translation 2 units down**: This means we will subtract 2 from the \(y\)-coordinate of each point.
2. **Translation 3 units to the right**: This means we will add 3 to the \(x\)-coordinate of each point.

Let's apply these translations to the given points \((-4, 2)\) and \((-4, 6)\).

1. For the point \((-4, 2)\):
- Translate 2 units down:
\[
y = 2 - 2 = 0
\]
- Translate 3 units to the right:
\[
x = -4 + 3 = -1
\]
- The new point is \((-1, 0)\).

2. For the point \((-4, 6)\):
- Translate 2 units down:
\[
y = 6 - 2 = 4
\]
- Translate 3 units to the right:
\[
x = -4 + 3 = -1
\]
- The new point is \((-1, 4)\).

Thus, the new points on the translated line are \((-1, 0)\) and \((-1, 4)\).