Table of Contents
How do you prove that every line segment has only one mid point?
Expert Answer:
- Suppose C and C’ are two mid points of segment AB.
- Then AC = AB.
- and AC’ = AB.
- AC = AC’ [Things which are equal to the same thing are equal to one another.]
- This is possible only when C and C’ coincide.
- Hence every line segment has one and only one midpoint.
Does a segment have a unique midpoint?
Theorem 9.2: The midpoint of a segment is unique. You’ll need a line segment; call it AB. You’ll also need two midpoints, which you can call M and N.
Does every line segment have a midpoint?
Only a line segment can have a midpoint. A line cannot since it goes on indefinitely in both directions, and so has no midpoint. A ray cannot because it has only one end, and hence no midpoint. When a line cuts another line into two equal parts it is called a bisector.
How do you know that a point is the midpoint of a segment?
To find the midpoint, draw the number line that contains points and . Then calculate the distance between the two points. In this case, the distance between and is . By dividing the distance between the two points by 2, you establish the distance from one point to the midpoint.
Is only one line can pass through a single point?
i) Only one line can pass through a single point. False because, we can draw infinite number of lines through a given point as shown below. ii) There are an infinite number of lines which pass through two distinct points. According to Postulate 2, a terminated line can be produced indefinitely.
Which axiom allows us to show that every line segment has a midpoint?
Axiom 4
A midpoint of a line segment AB is a point C on AB such that AC = BC and 2 · AC = AB. Theorem 2. Every line segment AB has exactly one midpoint. Now C is either between A and D, or between B and D If C is between A and D, then Axiom 4 says that AC + CD = AD.
Can a line segment have two distinct midpoints?
Answer and Explanation: A line segment cannot have two midpoints.
How many mid point does a segment have *?
one midpoint
A line segment has exactly one midpoint. In geometry, a line segment is a line with two endpoints.
How many midpoints does a segment Have explain?
How do you find the midpoint of a line segment?
Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.
How many lines pass two distinct points?
one line
So, only one line can pass through two distinct points.
How to find the midpoint of a line segment?
It defines the coordinate points of the midpoint of the line segment and can be found by taking the average of the coordinates of the given endpoints. The midpoint formula is used to determine the midpoint between the two given points.
What is the definition of midpoint in proofs?
What is the definition of midpoint in proofs? In geometry, the midpoint is defined as the point which divides the line segment into two equal parts. What does midpoint mean? Midpoint means a point which lies at or near the middle or equidistant from both ends of the line segment.
How do you find the midpoint of a triangle?
If P 1 (x 1, y 1) and P 2 (x 2, y 2) are the coordinates of two given endpoints, then the midpoint formula is given as: The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.
How do you use midpoint theorem in geometry?
The theory of midpoint theorem is used in the coordinate geometry stating that the midpoint of the line segment is an average of the endpoints. To solve an equation by the use of this Theorem, it is important that both the ‘x’ and the ‘y’ coordinates should be known.