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Perpendiculars and Parallels

How many rays...

Question

How many rays can be drawn with a given point as the initial point?
(a) One
(b) Two
(c) An unlimited number
(d) A limited number only

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Solution

(c) An unlimited number of rays can be drawn with a given point as the initial point. For example:

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Similar questions

Q. Write 'T' for true and 'F' for false in case of each of the following statements:
(i) Every point has a size.
(ii) A line segment has no length.
(iii) Every ray has a finite length.
(iv) The ray

\vec{A B}

is the same as the ray

\vec{B A}

.
(v) The line segment

\bar{A B}

is the same as the line segment

\bar{B A}

.
(vi) The line

\overset{\leftrightarrow}{A B}

is the same as the line

\overset{\leftrightarrow}{B A}

.
(vii) Two points A and B in a plane determine a unique line segment.
(viii) Two intersecting lines intersect at a point.
(ix) Two intersecting planes intersect at a point.
(x) If points A, B, C are collinear and points C, D, E are collineaer then the pints A,B, C, D, E are collinear.
(xi) One and only one ray can be drawn with a given end point.
(xii) One and only one line can be drawn to pass through two given points.
(xiii) An unlimited number of lines can be drawn to pass through a given point.

Q. Which of the following is a false statement?
(a) An infinite number of lines can be drawn through a given point.
(b) A unique line can be drawn through two given points.
(c) Ray

\underset{A B}{\to} = ray \underset{B A}{\to}

.
(d) A ray has one end-point.

Q. Match the following columns.

Column I	Column II
(a) How many lines can be drawn through one given point?	(p) One only
(b) How many lines can be drawn through two given points?	(q) Infinitely many
(c) How many end-points does a line $\overset{\leftrightarrow}{A B}$ have?	(r) Two only
(d) How many end-points does a line segment $A B$ have?	(s) None

(a) .......,
(b) .......,
(c) .......,
(d) .......,

A, B, C

D

are four point on a circle. How many chords can be drawn using only these points as the end points of the chord.

Q. How many circles can be drawn to pass through two given points?

(a) 1
(b) 2
(c) 0
(d) As many as possible

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