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 equation, we can use the fact that the midpoint of a line segment is the average of its endpoints.
In this case, we know that the midpoint C is equidistant from points A and B. We also know that AC is 17 units long.
So, if AB = 5x - 6, then AC would be half of AB, which gives us AC = (5x - 6)/2.
Setting AC equal to 17, we can write the equation as: (5x - 6)/2 = 17.
To solve for x, we can multiply both sides of the equation by 2 to eliminate the fraction: 5x - 6 = 34.
Next, we can add 6 to both sides of the equation: 5x = 40.
Finally, we divide both sides by 5 to solve for x: x = 8.
Therefore, the value of x is 8, which corresponds to option B.
For the second question, we are given that PQ is 8 units long and PR is 12 units long. To find the possible midpoints for line segment PQ, we can use the fact that the midpoint is equidistant from the endpoints.
So, we need to find a point that is equidistant from P and Q. Since PQ is a straight line, any point on the perpendicular bisector of PQ will be equidistant from P and Q.
To find the perpendicular bisector, we can draw a line segment from P to Q and use a compass to construct a perpendicular line through the midpoint of PQ.
The point where this perpendicular line intersects the line segment PQ is the possible midpoint for PQ.
By doing this construction, we can find the possible midpoints for line segment PQ.