Translations and Reflections Quick Check

Question

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Question
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

0 units
0 units

4 units
4 units

10 units
10 units

There is not enough information to measure the line segment.

Answer 1

To find the length of the line segment after the translation, we need to find the distance between the translated endpoints.

After the translation, the endpoint (6, 3) will move 3 units up, becoming (6, 6), and 4 units to the right, becoming (10, 6).

The other endpoint, (6, 7), will also move 3 units up, becoming (6, 10), and 4 units to the right, becoming (10, 10).

We can now find the length of the line segment using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((10 - 6)^2 + (10 - 6)^2)
Distance = √(4^2 + 4^2)
Distance = √(16 + 16)
Distance = √32
Distance ≈ 5.657 units

Therefore, the length of the line segment after the translation is approximately 5.657 units.