which of the following statement is false:1. only one line can be drawn through three collinear point2. A Ray has definitely length3. two lines which are in the same plane and do not intersect are called parallel line4. the point at which three or more lines meet is called the point of concurrence
Answers
Answer:
The given problem requires definitions of various terms.
(i) Line segment:
A line segment AB can be defined as the part of the line with end points A and B, whereA and B are the two points of the line.
It is denoted by
Let us take a line with two points A and B
This is a line AB
While,
This is a line segment AB.
(ii) Collinear points:
When three or more points lie on the same line; they are said to be collinear.
Example:
Let us take a line l. P, Q, R points lie on it.
So,
Here, P, Q and R are collinear points.
(iii) Parallel lines:
Two or more lines are said to be parallel to each other if there is no point of intersection between them.
For Example:
Since, there is no point of intersection between l and m, they are parallel.
(iv) Intersecting lines:
Two or more lines are said to be intersecting lines if they meet each other at a point or they have a common point.
For Example:
l and m are the two lines both passing through point O. Hence, they are intersecting lines.
(v) Concurrent lines:
Two or more lines are said to be concurrent if they all pass through a common point or there exist a point common to all of them.
For Example:
m, n, o and p are concurrent as they all have a common point O.
(vi) Ray:
A ray is defined as the part of the line with one end point such that it can be extended infinitely in the other direction.
It is represented by
For Example:
Here, is a ray as it has one end point A and it can be extended indefinitely in other direction.
(vii) Half-line:
A half-line can be defined as a part of the line which has one end point and extends indefinitely in the other direction. It is different from ray as the end point is not included in the half-line.
For example,
When A is included in the part, then it is called a ray AB, but when A is not included then is called a half-line AB.
Page No 9.8:
Question 2:
(i) How many lines can pass through a given point?
(ii) In how many points can two distinct lines at the most intersect?
ANSWER:
(i) Let us take a point A.
If we try to draw lines passing through this point A, we can see that we can draw many lines.
Therefore, infinite number of lines can pass through a given point.
(ii) Let us take two lines l and m, and intersect them.
As, we can see here the two lines have only one point in common that is O.
Therefore, there is only one point where two distinct lines can intersect.
Page No 9.8:
Question 3:
(i) Given two points P and Q, find how many line segments do they deter-mine.
(ii) Name the line segments determined by the three collinear points P, Q and R.
ANSWER:
(i) In this problem we are given two points P and Q.
If we try to join these two points through a line segment, we can see that there can be only one such line segment PQ.
Therefore, given two points, only one line segment is determined by them.
(ii) In the given problem, we are given three collinear points P, Q and R. Collinear points lie on the same line, so they can be represented as
So, the various line segments determined here are PQ, QR and PR.
Page No 9.8:
Question 4:
Write the turth value (T/F) of each of the following statements:
(i) Two lines intersect in a point.
(ii) Two lines may intersect in two points.
(iii) A segment has no length.
(iv) Two distinct points always determine a line.
(v) Every ray has a finite length.
(vi) A ray has one end-point only.
(vii) A segment has one end-point only.
(viii) The ray AB is same as ray BA.
(ix) Only a single line may pass through a given point.
Answer:
only one line can be drought root 3 colinor point