To determine the length of the line segment after the translation, we first need to find the length of the original line segment.
The endpoints of the line segment are (6, 3) and (6, 7). In this case, both x-coordinates are the same (6), indicating that the line segment is vertical.
To find the length of the line segment, we calculate the distance between the two endpoints using the formula: \[ \text{Length} = |y_2 - y_1| \] where \((x_1, y_1) = (6, 3)\) and \((x_2, y_2) = (6, 7)\). Substituting in the values: \[ \text{Length} = |7 - 3| = |4| = 4 \text{ units} \]
Next, we translate the line segment 3 units up and 4 units to the right. The new endpoints after the translation will be:
- The point (6, 3) translates to (6 + 4, 3 + 3) = (10, 6)
- The point (6, 7) translates to (6 + 4, 7 + 3) = (10, 10)
Now, we have the new endpoints: (10, 6) and (10, 10).
To find the length of the new line segment, we apply the same distance formula: \[ \text{Length} = |y_2 - y_1| = |10 - 6| = |4| = 4 \text{ units} \]
Thus, the length of the line segment after the translation remains 4 units.
Therefore, the correct response is 4 units.
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