AB is a line segment. Construct PQ if PQ is twice the length of AB. [3 MARKS]

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Solution

Constructing PQ: 1 Mark
Steps: 2 Mark

Steps for constructing PQ based on the length of AB:
(i) Let AB be the line segment.

(ii) Adjust the compass up to the length of AB.

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

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

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

PQ 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 $¯ ¯¯¯¯¯¯ ¯ A B$ .

Raghu walked along a path AB in 5 minutes. After some time he walked along the path PQ which happens to be twice as long as AB.
Construct the line PQ. [3 MARKS]

Q. Two line segments, AB of length 7cm and PQ of length 7cm are drawn on a sheet. The relation between the two line segments is/are:

Q. Given

¯ A B = 3.9

cm,construct

¯ P Q

such that the length of

¯ P Q

is twice that of

¯ A B

Q. If PQ is the perpendicular bisector of line segment AB then the length of PQ will be.

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