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?

Well, if we want the midpoint of line segment PQ to be P, that would mean P would have to be halfway between Q and the midpoint. Since PQ is 8 units long, that means the midpoint would have to be 4 units away from both P and Q. But in that case, there would be no way for PR to be 12 units long, so P cannot be the midpoint.

If we want the midpoint of line segment PQ to be Q, that would mean Q would have to be halfway between P and the midpoint. Since PQ is 8 units long, that means the midpoint would have to be 4 units away from both Q and P. But in that case, there would be no way for PR to be 12 units long, so Q cannot be the midpoint.

Therefore, the only possible midpoint for line segment PQ is between P and Q.

To solve the first problem, we can use the fact that the midpoint of a line segment divides the segment into two equal parts. Since AC is equal to 17 and AB is given as 5x-6, we can set up an equation:

17 = (5x-6)/2

To solve for x, we first multiply both sides of the equation by 2 to eliminate the fraction:

34 = 5x - 6

Next, we add 6 to both sides to isolate the term with x:

40 = 5x

Finally, we divide both sides by 5 to solve for x:

x = 40/5

Simplifying, we get:

x = 8

Therefore, the value of x is 8, corresponding to option B.

For the second problem, we are given that the coordinate of point P is 2 and lengths PQ and PR are 8 and 12 respectively. To find the possible midpoints for line segment PQ, we need to find the coordinates of the midpoint.

The midpoint of a line segment can be found by averaging the corresponding coordinates of the two endpoints. In this case, we have the x-coordinate of point P as 2 and the x-coordinate of point Q as an unknown value, say x. So, the x-coordinate of the midpoint would be (2 + x)/2.

Similarly, for the y-coordinate, we have no given information. Therefore, we can represent the y-coordinate of point Q as an unknown value, say y. The y-coordinate of the midpoint would then be (0 + y)/2.

So, the possible midpoints for line segment PQ would be the coordinates ( (2 + x)/2 , (0 + y)/2 ), where x and y can be any values that satisfy the given conditions.

Unfortunately, without further information, we cannot determine the exact possible midpoints.