Line segment AB has a midpoint C
Help?
If AC=17 and AB = 5x-6, then find the value of x
A. 34
B.8
C. 23/5
D. 20
Answer: D
2.
Suppose the coordinate of p=2 and PQ=8 and PR=12. Whare are the possible mid point for line segment PQ?
To find the value of x in the given scenario, we need to use the concept of midpoint. The midpoint of a line segment is the point that divides the line segment into two equal parts. In this case, the line segment AB has a midpoint at C.
We are given that AC = 17 and AB = 5x - 6. To find the value of x, we need to use the midpoint formula, which states that the coordinates of the midpoint (C) can be found by averaging the coordinates of the endpoints (A and B).
The midpoint formula can be written as (x1 + x2)/2 and (y1 + y2)/2 for a line segment with endpoints (x1, y1) and (x2, y2).
In our case, since we are dealing with a line segment on a 1-dimensional number line, only the x-coordinate is relevant. So, we can rewrite the formula as (x1 + x2)/2.
The x-coordinate of point A is 5x - 6, and the x-coordinate of point C is the value we are trying to find.
Using the midpoint formula, we can set up the following equation:
[(5x - 6) + 0]/2 = 17
Simplifying the equation:
5x - 6 = 34
Adding 6 to both sides:
5x = 40
Dividing both sides by 5:
x = 8
Therefore, the value of x is 8.
So, the correct answer is B. 8.
2. To find the possible midpoints for line segment PQ with coordinates p = 2 and PQ = 8, we need to understand the concept of a midpoint.
The midpoint of a line segment is the point that divides the line segment into two equal parts. To find the midpoint, we need to find a point that is equidistant from both endpoints.
Since the coordinate of point P is 2, the coordinate of point Q is 2 + PQ, which is 2 + 8 = 10.
To find possible midpoints, we need to find a point that is equidistant from both 2 and 10. Since the distance from 2 to a midpoint would be equal to the distance from the midpoint to 10, we can calculate the distance from 2 to the midpoint.
The distance from 2 to the midpoint would be half of the total distance between 2 and 10.
The total distance between 2 and 10 is 10 - 2 = 8 units.
Half of 8 units is 8/2 = 4 units.
Therefore, the possible midpoints for line segment PQ would be 4 units away from 2 in either direction: 2 - 4 = -2 and 2 + 4 = 6.
So, the possible midpoints for line segment PQ are -2 and 6.