Question

A line contains the points (−4, 2) and (−4, 6) . The line is translated 3 units to the right and 2 units down. What are the new points on the translated line? The new point for (−4, 2) is: (). The new point for (−4, 6) is: ().

Answer 1

To translate a point, you add to the x-coordinate for a rightward movement and add to the y-coordinate for a downward movement.

Given the original points are \((-4, 2)\) and \((-4, 6)\):

1. For the point \((-4, 2)\):
- Translate 3 units to the right: \(-4 + 3 = -1\)
- Translate 2 units down: \(2 - 2 = 0\)

So, the new point is \((-1, 0)\).

2. For the point \((-4, 6)\):
- Translate 3 units to the right: \(-4 + 3 = -1\)
- Translate 2 units down: \(6 - 2 = 4\)

So, the new point is \((-1, 4)\).

Thus, the translated points are:
- The new point for \((-4, 2)\) is: \((-1, 0)\).
- The new point for \((-4, 6)\) is: \((-1, 4)\).