To find the length of the line segment after the translation, we first need to determine the length of the original line segment between the endpoints (6, 3) and (6, 7).
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Calculate the length of the original segment: The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For the endpoints (6, 3) and (6, 7): \[ d = \sqrt{(6 - 6)^2 + (7 - 3)^2} = \sqrt{0 + (4)^2} = \sqrt{16} = 4 \text{ units} \]
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Determine the translation: The translation involves moving the segment 3 units up and 4 units to the right.
- The new coordinates after translation will be:
- Starting point (6, 3) translates to (6 + 4, 3 + 3) = (10, 6)
- Ending point (6, 7) translates to (6 + 4, 7 + 3) = (10, 10)
- The new coordinates after translation will be:
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Calculate the length of the translated segment: Using the length formula again for the new endpoints (10, 6) and (10, 10): \[ d = \sqrt{(10 - 10)^2 + (10 - 6)^2} = \sqrt{0 + (4)^2} = \sqrt{16} = 4 \text{ units} \]
The length of the line segment after the translation is still 4 units.
So, the correct response is 4 units.