To determine the length of the line segment after translating it, we first need to find its original length and then check if the translation affects that length.
The original endpoints of the line segment are (6, 3) and (6, 7). To calculate the length of the segment, we can use the distance formula. However, since both points have the same x-coordinate (6), we can simply find the difference in the y-coordinates:
\[ \text{Length} = |y_2 - y_1| = |7 - 3| = 4 \text{ units} \]
Next, we apply the translation of 3 units up and 4 units to the right:
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Translating (6, 3):
- Move 3 units up: \(3 + 3 = 6\)
- Move 4 units to the right: \(6 + 4 = 10\)
- New point: (10, 6)
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Translating (6, 7):
- Move 3 units up: \(7 + 3 = 10\)
- Move 4 units to the right: \(6 + 4 = 10\)
- New point: (10, 10)
Now, we calculate the length of the new line segment with endpoints (10, 6) and (10, 10):
Again, since both points share the same x-coordinate (10), we calculate the difference in the y-coordinates:
\[ \text{New Length} = |10 - 6| = 4 \text{ units} \]
The length of the line segment after the translation remains 4 units.
So the answer is 4 units.
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