If a line segment with endpoints (6, 3)

Question

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

4 units
4 units

10 units
10 units

0 units
0 units

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

Answer 1

To find the length of the line segment, we first need to determine its original length. The endpoints of the line segment are (6, 3) and (6, 7).

The length of a vertical line segment can be calculated using the formula for the distance between two points, specifically focusing on their y-coordinates since the x-coordinates are the same:

$$\text{Length}=|y_2-y_1|=|7-3|=4\text{ units}$$

Next, we will apply the translation that moves the line segment 3 units up and 4 units to the right. This will change the endpoints:

• The original point (6, 3) becomes: $$(6+4,3+3)=(10,6)$$

• The original point (6, 7) becomes: $$(6+4,7+3)=(10,10)$$

Now the new endpoints after the translation are (10, 6) and (10, 10). We can again calculate the length of this new line segment:

$$\text{New Length}=|y_2-y_1|=|10-6|=4\text{ units}$$

So, after the translation, the length of the line segment remains 4 units.

Therefore, the answer is:

4 units