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 equation AB = 5x - 6, where AC is given as 17, we need to use the fact that C is the midpoint of AB.
The midpoint formula states that the coordinates of the midpoint (C) of a line segment are the average of the coordinates of its endpoints (A and B).
In this case, if AC = 17, then CB also equals 17 since C is the midpoint of AB.
We can set up an equation using the midpoint formula:
AC + CB = AB
17 + 17 = 5x - 6
34 = 5x - 6
Adding 6 to both sides:
40 = 5x
Dividing both sides by 5:
8 = x
Therefore, the value of x is 8, which corresponds to option B.
For the second question, if the coordinate of P is 2 and PQ = 8, we can find the possible midpoint(s) of line segment PQ.
The midpoint of a line segment is the average of the coordinates of its endpoints. In this case, we need to find the average of the coordinates of P and Q.
Since the coordinate of P is given as 2, and the length of PQ is given as 8, we can find the possible midpoint(s) by adding half of the length of PQ to the coordinate of P.
Thus, the midpoint(s) of PQ will be:
2 + (8/2) = 2 + 4 = 6
Therefore, the possible midpoint(s) for line segment PQ is 6.