Question

the midpoint of a horizontal line segment is at x=1 if the length of the line segment is 10.5. what absolute value equation could be used to find the x value of the endpoints

Answer 1

Answer: -4.25 ≤ x ≤ 6.25

Step-by-step explanation:

The midpoint of a segment is located at the same distance of each of the endpoints of the segment.

The midpoint is at x = 1.

The length of the segment is 10.5, if we divide it by two we have:

10.5/2 = 5.25

Now, if we want the endpoints to be at the same distance of the midpoint, then the endpoints will be:

Xmax = midpoint + 5.25

Xmin = midpoint - 5.25

Then the extremes are:

Xmax = 1 + 5.25 = 6.25

Xmin = 1 - 5.25 = -4.25

Then this segment can be written as:

Xmin ≤ x ≤ Xmax

-4.25 ≤ x ≤ 6.25