Given AB of length 3-9 cm- construct PQ such that the length of PQ is twice that of AB- Verify by measurement-X OHint- construct PX such that length of PX - length of AB- then cut off XQ such that XQ also has the length of AB-

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Standard VI

Mathematics

Construction of a Line Segment

Given AB of l...

Question

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.)

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Solution

A line segment can be drawn such that the length of is twice that of as follows.

(1) Draw a line l and mark a point P on it and let AB be the given line segment of 3.9 cm.

(2) By adjusting the compasses up to the length of AB, draw an arc to cut

the line at X, while taking the pointer of compasses at point P.

(3) Again put the pointer on point X and draw an arc to cut line l again at

Q.

is the required line segment. By ruler, the length of can be measured which comes to 7.8 cm.

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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

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 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.

Given $¯ ¯¯¯¯¯¯ ¯ A B$ of length $7.3 c m$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ of length $3.4 c m$ , construct a line segment $¯ ¯¯¯¯¯¯¯ ¯ X Y$ such that the length of $¯ ¯¯¯¯¯¯¯ ¯ X Y$ is equal to the difference between the lengths of $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ . Verify by measurement

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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.)

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.)