A line segment is translated 3 units down and 1 unit to the left. One of the endpoints after the translation is (5, 8)

Question

. What was this point before the translation?

Answer 1

To find the original endpoint of the line segment before the translation, we need to reverse the translation applied to that point.

The translation that was applied is:

• 3 units down (which corresponds to subtracting 3 from the y-coordinate)
• 1 unit to the left (which corresponds to subtracting 1 from the x-coordinate)

Given the point after the translation is \((5, 8)\), we will reverse the translation as follows:

1. To undo the 3 units down, we add 3 to the y-coordinate: \[ y = 8 + 3 = 11 \]

2. To undo the 1 unit to the left, we add 1 to the x-coordinate: \[ x = 5 + 1 = 6 \]

Therefore, the original endpoint before the translation is: \[ (6, 11) \]

So, the point before the translation was \((6, 11)\).