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If a line segment with endpoints (6, 3)

and (6, 7)
is translated 3 units up and 4 units to the right, how long is the line segment after the translation?(1 point)
Responses

There is not enough information to measure the line segment.
There is not enough information to measure the line segment.

10 units
10 units

0 units
0 units

4 units
4 units

1 answer

To find the length of the line segment after the translation, we first need to calculate the original length of the line segment.

The endpoints of the line segment are (6, 3) and (6, 7). Since the x-coordinates are the same, this is a vertical line segment. The length of the line segment can be calculated as the difference in the y-coordinates:

Length = |y2 - y1| = |7 - 3| = 4 units.

Now, we apply the translation: 3 units up and 4 units to the right.

  • Translating (6, 3) 3 units up gives (6, 3 + 3) = (6, 6).
  • Translating (6, 7) 3 units up gives (6, 7 + 3) = (6, 10).

Now, the new endpoints after the translation are (10, 6) and (10, 10). The length of the translated line segment is calculated in the same way:

Length = |10 - 6| = 4 units.

Therefore, the length of the line segment after the translation is still 4 units.

The correct response is 4 units.