Given some line segment, whose length you do not know, construct such that the length of is twice that of .

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Solution

The following steps will be followed to construct a line segment such that the length of is twice that of .

(1) Let be the given line segment.

(2) Adjust the compasses up to the length of .

(3) Draw any line l and mark a point P on it.

(4) Put the pointer on P and without changing the setting of compasses, draw an arc to cut the line segment at point X.

(5) Now, put the pointer on point X and again draw an arc with the same radius as before, to cut the line l at point Q.

is the required line segment.

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Question 2

Given some line segment $¯ ¯¯¯¯¯¯ ¯ A B$ , whose length you do not know, construct $¯ ¯¯¯¯¯¯ ¯ P Q$ such that the length of $¯ ¯¯¯¯¯¯ ¯ P Q$ is twice that of $¯ ¯¯¯¯¯¯ ¯ A B$ .

Given of length 3.9 cm, construct such that the length of is twice that of. Verify by measurement.

(Hint: constructsuch that length of= length of; then cut offsuch thatalso has the length of.)

Question 4

Given $¯ ¯¯¯¯¯¯ ¯ A B$ of length 3.9 cm, construct $¯ ¯¯¯¯¯¯ ¯ P Q$ such that the length $¯ ¯¯¯¯¯¯ ¯ P Q$ is twice that of AB . Verify by measurement.

(Hint: Construct $¯ ¯¯¯¯¯¯¯ ¯ P X$ such that length of $¯ ¯¯¯¯¯¯¯ ¯ P X$ = length of $¯ ¯¯¯¯¯¯ ¯ A B$ ;
then cut off $¯ ¯¯¯¯¯¯¯ ¯ X Q$ such that $¯ ¯¯¯¯¯¯¯ ¯ X Q$ also has the length of $¯ ¯¯¯¯¯¯ ¯ A B$ .)

Q. Given

¯ A B = 3.9

cm,construct

¯ P Q

such that the length of

¯ P Q

is twice that of

¯ A B

Given of length 7.3 cm and of length 3.4 cm, construct a line segment such that the length of is equal to the difference between the lengths of and. Verify by measurement.

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